Books

We pub­lish two series of pro­ceed­ings and mono­graphs, Geo­metry & To­po­logy Mono­graphs and the new­er The Open Book Series™. These volumes are pub­lished free on­line, while prin­ted cop­ies are avail­able through print-on-de­mand.

Books order form  

You can use this books or­der form to pro­duce a filled-out form that you can print and mail to us with your pay­ment.

Book proposals

If you have a volume that would be suit­able for one of our series, we’d like to hear about it. To find out more, please read about our book-pub­lish­ing ser­vices.

logo for open access

The Open Book Series™ OA

msp.​org/​obs  

The Open Book Series is a series of pro­ceed­ings and mono­graphs with a high qual­ity of con­tent. Each volume can be read freely on­line, while prin­ted cop­ies are avail­able for pur­chase.

logo for open access

Gauge Theory and Low-Dimensional Topology: Progress and Interaction OA

John A. Baldwin, Hans U. Boden, John B. Etnyre, and Liam Watson (editors)
OBS 5 (2022) xii+332
msp.​org/​obs/​2022/​5  
cover for Gauge Theory and Low-Dimensional Topology: Progress and Interaction

This volume is a pro­ceed­ings of the sixth Ban­ff In­ter­na­tion­al Re­search Sta­tion work­shop on “In­ter­ac­tions of gauge the­ory with con­tact and sym­plect­ic to­po­logy in di­men­sions 3 and 4”, held in 2020 over the in­ter­net. The volume con­tains six­teen ref­er­eed pa­pers, with an em­phas­is on new de­vel­op­ments and in­ter­con­nec­tions of gauge the­ory, low-di­men­sion­al to­po­logy, con­tact and sym­plect­ic to­po­logy. It is rep­res­ent­at­ive of the high level of talks and res­ults presen­ted at the In­ter­ac­tions work­shops over the years since its in­cep­tion in 2007.

Pricing and Sales  
logo for open access

ANTS XIV: Proceedings of the Fourteenth Algorithmic Number Theory Symposium (U Auckland, 2020) OA

Steven D. Galbraith (editor)
OBS 4 (2020) viii+422
msp.​org/​obs/​2020/​4  
cover for ANTS XIV: Proceedings of the Fourteenth Algorithmic Number Theory Symposium <q>(U Auckland, 2020)</q>

The Al­gorithmic Num­ber The­ory Sym­posi­um (ANTS), held bi­en­ni­ally since 1994, is the premi­er in­terna­tion­al for­um for re­search in com­pu­ta­tion­al and al­gorithmic num­ber the­ory. ANTS is de­voted to al­gorithmic as­pects of num­ber the­ory, in­clud­ing ele­ment­ary, al­geb­ra­ic, and ana­lyt­ic num­ber the­ory, the geo­metry of num­bers, arith­met­ic al­geb­ra­ic geo­metry, the the­ory of fi­nite fields, and cryp­to­graphy.

This volume is the pro­ceed­ings of the four­teenth ANTS meet­ing, which took place 29 June to 4 Ju­ly 2020 via video con­fer­ence, the plans for hold­ing it at the Uni­versity of Auck­land, New Zea­l­and, hav­ing been dis­rup­ted by the COV­ID-19 pan­dem­ic. The volume con­tains re­vised and ed­ited ver­sions of 24 ref­er­eed pa­pers and one in­vited pa­per presen­ted at the con­fer­ence.

Pricing and Sales  
logo for open access

Poincaré duality in dimension 3 OA

Jonathan Hillman
OBS 3 (2020) xiv+149
msp.​org/​obs/​2020/​3  
cover for Poincaré duality in dimension 3

Poin­caré du­al­ity is cent­ral to the un­der­stand­ing of man­i­fold to­po­logy. Di­men­sion 3 is crit­ic­al in vari­ous re­spects, be­ing between the known ter­rit­ory of sur­faces and the wil­der­ness mani­fest in di­men­sions ≥ 4. The main thrust of 3-man­i­fold to­po­logy for the past half cen­tury has been to show that as­pher­ic­al closed 3-man­i­folds are de­term­ined by their fun­da­ment­al groups. Re­l­at­ively little at­ten­tion has been giv­en to the ques­tion of which groups arise. This book is the first com­pre­hens­ive ac­count of what is known about PD3-com­plexes, which mod­el the ho­mo­topy types of closed 3-man­i­folds, and PD3-groups, which cor­res­pond to as­pher­ic­al 3-man­i­folds. In the first half we show that every P2-ir­re­du­cible PD3-com­plex is a con­nec­ted sum of in­decom­pos­ables, which are either as­pher­ic­al or have vir­tu­ally free fun­da­ment­al group, and largely de­term­ine the lat­ter class. The pic­ture is much less com­plete in the as­pher­ic­al case. We sketch sev­er­al pos­sible aproaches for tack­ling the cent­ral ques­tion, wheth­er every PD3-group is a 3-man­i­fold group, and then ex­plore prop­er­ties of sub­groups of PD3-groups, uni­fy­ing many res­ults of 3-man­i­fold to­po­logy. We con­clude with an ap­pendix list­ing over 60 ques­tions. Our gen­er­al ap­proach is to prove most as­ser­tions which are spe­cific­ally about Poin­caré du­al­ity in di­men­sion 3, but oth­er­wise to cite stand­ard ref­er­ences for the ma­jor sup­port­ing res­ults.

Tar­get read­er­ship: Gradu­ate stu­dents and math­em­aticians with an in­terest in low-di­men­sion­al to­po­logy.

Pricing and Sales  
logo for open access

ANTS XIII: Proceedings of the Thirteenth Algorithmic Number Theory Symposium (U Wisconsin, 2018) OA

Renate Scheidler and Jonathan Sorenson (editors)
OBS 2 (2018) x+478
msp.​org/​obs/​2019/​2  
cover for ANTS XIII: Proceedings of the Thirteenth Algorithmic Number Theory Symposium <q>(U Wisconsin, 2018)</q>

The Al­gorithmic Num­ber The­ory Sym­posi­um (ANTS), held bi­en­ni­ally since 1994, is the premi­er inter- na­tion­al for­um for re­search in com­pu­ta­tion­al num­ber the­ory. ANTS is de­voted to al­gorithmic as­pects of num­ber the­ory, in­clud­ing ele­ment­ary, al­geb­ra­ic, and ana­lyt­ic num­ber the­ory, the geo­metry of num­bers, arith­met­ic al­geb­ra­ic geo­metry, the the­ory of fi­nite fields, and cryp­to­graphy.

This volume is the pro­ceed­ings of the thir­teenth ANTS meet­ing, held Ju­ly 16–20, 2018, at the Uni­versity of Wis­con­sin-Madis­on. It in­cludes re­vised and ed­ited ver­sions of 28 ref­er­eed pa­pers presen­ted at the con­fer­ence.

Pricing and Sales  
logo for open access

ANTS X: Proceedings of the Tenth Algorithmic Number Theory Symposium (UC San Diego, 2012) OA

Everett Howe and Kiran Kedlaya (editors)
OBS 1 (2013) x+585
msp.​org/​obs/​2013/​1  
cover for ANTS X: Proceedings of the Tenth Algorithmic Number Theory Symposium <q>(UC San Diego, 2012)</q>

The Al­gorithmic Num­ber The­ory Sym­posi­um (ANTS), held bi­en­ni­ally since 1994, is the premi­er in­ter­na­tion­al for­um for re­search in com­pu­ta­tion­al num­ber the­ory. ANTS is de­voted to al­gorithmic as­pects of num­ber the­ory, in­clud­ing ele­ment­ary, al­geb­ra­ic, and ana­lyt­ic num­ber the­ory, the geo­metry of num­bers, arith­met­ic al­geb­ra­ic geo­metry, the the­ory of fi­nite fields, and cryp­to­graphy.

This volume is the pro­ceed­ings of the tenth ANTS meet­ing, held Ju­ly 9–13, 2012, at the Uni­versity of Cali­for­nia, San Diego. It in­cludes re­vised and ed­ited ver­sions of the 25 ref­er­eed pa­pers presen­ted at the con­fer­ence, to­geth­er with ex­ten­ded ab­stracts of two of the five in­vited talks.

Pricing and Sales  
logo for open access

Geometry & Topology Monographs OA

msp.​org/​gtm  

The GTM series is in­ten­ded for re­search mono­graphs, ref­er­eed con­fer­ence pro­ceed­ings, and sim­il­ar col­lec­tions. Each volume can be read freely on­line, while prin­ted cop­ies are avail­able for pur­chase.

logo for open access

Interactions between low-dimensional topology and mapping class groups (Max Plank, Bonn, 2013) OA

R. Inanç Baykur, John Etnyre and Ursula Hamenstädt (editors)
GTM 19 (2015) viii+413
msp.​org/​gtm/​2015/​19  
cover for Interactions between low-dimensional topology and mapping class groups <q>(Max Plank, Bonn, 2013)</q>

There has been a long his­tory of rich and subtle con­nec­tions between low-di­men­sion­al to­po­logy, map­ping class groups and geo­met­ric group the­ory. From 1 to 5 Ju­ly 2013, the con­fer­ence “In­ter­ac­tions between low di­men­sion­al to­po­logy and map­ping class groups,” held at the Max Planck In­sti­tute for Math­em­at­ics in Bonn, high­lighted these di­verse con­nec­tions and fostered new and un­ex­pec­ted col­lab­or­a­tions between re­search­ers in these areas.

The pro­ceed­ings for this con­fer­ence aim to fur­ther draw at­ten­tion to the beau­ti­ful math­em­at­ics emer­ging from di­verse in­ter­ac­tions between these areas. The art­icles col­lec­ted in this volume, in ad­di­tion to gath­er­ing new res­ults, also con­tain ex­pos­i­tions and sur­veys of the latest de­vel­op­ments in vari­ous act­ive areas of re­search at the in­ter­face of map­ping class groups of sur­faces and the to­po­logy and geo­metry of 3- and 4-di­men­sion­al man­i­folds. Many open prob­lems and new dir­ec­tions for re­search are dis­cussed.

Pricing and Sales  
logo for open access

Proceedings of the FreedmanFest (Berkeley, 2011) OA

Rob Kirby, Vyacheslav Krushkal and Zhenghan Wang (editors)
GTM 18 (2012) viii+450
msp.​org/​gtm/​2012/​18  
cover for Proceedings of the FreedmanFest <q>(Berkeley, 2011)</q>

This volume is ded­ic­ated to Mike Freed­man on the oc­ca­sion of his 60th birth­day. It con­tains pa­pers on a wide vari­ety of top­ics in To­po­logy and Phys­ics and is based on two con­fer­ences that were held in 2011. The Con­fer­ence on Low-Di­men­sion­al Man­i­folds and High-Di­men­sion­al Cat­egor­ies, in hon­or of Mi­chael Freed­man, was held at UC Berke­ley on June 6–10, 2011. It fea­tured talks by Yakov Eli­ash­berg, Ron Fin­tushel, Dav­id Gay, Camer­on Gor­don, Sergei Gukov, Ko Honda, Mi­chael Hutch­ings, Slava Krushkal, Yanki Lekili, Scott Mor­ris­on, Frank Quinn, Mar­tin Schar­le­mann, Rob Schnei­der­m­an, Cath­ar­ina Strop­pel, Clif­ford Taubes, Peter Teich­ner, Ben Web­ster, Kat­rin Wehrheim, and Ed­ward Wit­ten. The or­gan­iz­ing com­mit­tee con­sisted of Ian Agol, Ro­bi­on Kirby, Slava Krushkal, Peter Teich­ner, Abi­gail Thompson, and Kev­in Walk­er.

The Freed­man Sym­posi­um was held at the Kavli In­sti­tute for The­or­et­ic­al Phys­ics in Santa Bar­bara on April 15–17, 2011. In­vited lec­tures were giv­en by Scott Aaron­son, Sank­ar Das Sarma, Ed­die Far­hi, Mat­thew Fish­er, Dan Freed, Matt Hast­ings, Charlie Kane, Alexei Kit­aev, Steve Kiv­el­son, Laci Lovasz, An­dreas Lud­wig, John Man­fer­del­li, Greg Moore, Chet­an Nayak, John Preskill, Xiao­l­i­ang Qi, Peter Shor, Kir­ill Shten­gel, Steve Si­mon, and Xiao-Gang Wen. The con­fer­ence was or­gan­ized by Chet­an Nayak and Zhenghan Wang.

The pub­lic­a­tion of this volume and the con­fer­ences were sup­por­ted in part by Zheng-Xu He, the Na­tion­al Sci­ence Found­a­tion, and Mi­crosoft Sta­tion Q.

Pricing and Sales  
logo for open access

Lectures on Poisson geometry (Trieste, 2005) OA

Tudor Ratiu, Alan Weinstein and Nguyen Tien Zung (editors)
GTM 17 (2011) xiv+503
msp.​org/​gtm/​2011/​17  
cover for Lectures on Poisson geometry <q>(Trieste, 2005)</q>

Pois­son geo­metry is a rap­idly grow­ing sub­ject, with many in­ter­ac­tions and ap­plic­a­tions in areas of math­em­at­ics and phys­ics, such as clas­sic­al dif­fer­en­tial geo­metry, Lie the­ory, non­com­mut­at­ive geo­metry, in­teg­rable sys­tems, flu­id dy­nam­ics, quantum mech­an­ics, and quantum field the­ory. Re­cog­niz­ing the role played by Pois­son geo­metry and the sig­ni­fic­ant re­search it has gen­er­ated, the Ab­dus Salam In­ter­na­tion­al Centre for The­or­et­ic­al Phys­ics in Trieste, Italy, sponsored a 3-week sum­mer activ­ity on this sub­ject (Ju­ly 4–22 2005) in or­der to bring it to the at­ten­tion of sci­ent­ists and stu­dents from de­vel­op­ing coun­tries. There was an over­whelm­ing re­sponse to this pro­gram, which brought to­geth­er more than 150 par­ti­cipants from all over the world with var­ied back­grounds, from gradu­ate stu­dents to ex­perts.

The pro­gram con­sisted of a two-week in­tens­ive school com­pris­ing 10 minicourses, fol­lowed by a week-long in­ter­na­tion­al re­search con­fer­ence. The lec­tur­ers at the school were asked to turn their notes in­to sec­tions of a book that could serve as a quick in­tro­duc­tion to the cur­rent state of re­search in Pois­son geo­metry. We hope that the present volume will be use­ful to people who want to learn about Pois­son geo­metry and its ap­plic­a­tions.

Pricing and Sales  
logo for open access

New topological contexts for Galois theory and algebraic geometry (Banff, 2008) OA

Andrew Baker and Birgit Richter (editors)
GTM 16 (2009) x+593
msp.​org/​gtm/​2009/​16  
cover for New topological contexts for Galois theory and algebraic geometry <q>(Banff, 2008)</q>

In the late twen­ti­eth cen­tury, stable ho­mo­topy the­ory ex­pan­ded rap­idly and be­came in­creas­ingly soph­ist­ic­ated in de­fin­ing ho­mo­top­ic­ally in­vari­ant al­geb­ra­ic ma­chinery as­so­ci­ated with mul­ti­plic­at­ive co­homo­logy the­or­ies and their in­tern­al op­er­a­tions. In­puts to these de­vel­op­ments have in­cluded es­tab­lished math­em­at­ic­al ideas from sub­jects such as al­geb­ra­ic geo­metry and num­ber the­ory. The work­shop “New To­po­lo­gic­al Con­texts for Galois The­ory and Al­geb­ra­ic Geo­metry” brought to­geth­er to­po­lo­gists in­volved in de­vel­op­ing or us­ing these new tech­niques and al­lowed for the in­ter­ac­tions with oth­er sub­ject areas by in­clud­ing non-to­po­lo­gist par­ti­cipants who would con­trib­ute to this.

Pricing and Sales  
logo for open access

Compactness and gluing theory for monopoles OA

Kim A. Frøyshov
GTM 15 (2008) viii+198
msp.​org/​gtm/​2008/​15  
cover for Compactness and gluing theory for monopoles

This book is de­voted to the study of mod­uli spaces of Seiberg–Wit­ten mono­poles over spinc Rieman­ni­an 4-man­i­folds with long necks and/or tu­bu­lar ends. The ori­gin­al pur­pose of this work was to provide ana­lyt­ic­al found­a­tions for a cer­tain con­struc­tion of Flo­er ho­mo­logy of ra­tion­al ho­mo­logy 3-spheres; this is car­ried out in “Mono­pole Flo­er ho­mo­logy for ra­tion­al ho­mo­logy 3-spheres” [arX­iv 0809.4842]. However, along the way the pro­ject grew, and, ex­cept for some of the trans­vers­al­ity res­ults, most of the the­ory is de­veloped more gen­er­ally than is needed for that con­struc­tion. Flo­er ho­mo­logy it­self is hardly touched upon in this book, and, to com­pensate for that, I have in­cluded an­oth­er ap­plic­a­tion of the ana­lyt­ic­al ma­chinery, namely a proof of a “gen­er­al­ized blow-up for­mula” which is an im­port­ant tool for com­put­ing Seiberg–Wit­ten in­vari­ants.

The book is di­vided in­to three parts. Part 1 is al­most identic­al to my pa­per “Mono­poles over 4-man­i­folds con­tain­ing long necks, I” [Geom. To­pol. 9 (2005) 1–93]. The oth­er two parts con­sist of pre­vi­ously un­pub­lished ma­ter­i­al. Part 2 is an ex­pos­it­ory ac­count of glu­ing the­ory in­clud­ing ori­ent­a­tions. The main nov­el­ties here may be the for­mu­la­tion of the glu­ing the­or­em, and the ap­proach to ori­ent­a­tions. In Part 3 the ana­lyt­ic­al res­ults are brought to­geth­er to prove the gen­er­al­ized blow-up for­mula.

Pricing and Sales  
logo for open access

The Zieschang Gedenkschrift OA

Michel Boileau, Martin Scharlemann and Richard Weidmann (editors)
GTM 14 (2008) xiv+567
msp.​org/​gtm/​2008/​14  
cover for The Zieschang Gedenkschrift

This volume is ded­ic­ated to Hein­er Zi­eschang, who has been a teach­er, ment­or and friend to us and to most of those that have con­trib­uted their work con­tained in this volume.

Con­tri­bu­tions by: Jochen Abhau, Carl-Friedrich Bödigheimer, Anne Bauval, Se­meon Bogatyi, Oleg Bogo­pol­ski, Michel Boileau, Steve Boy­er, Daryl Cooper, Ralf Ehren­fried, Jan Fricke, Olga Frolk­ina, Claude Hay­at, C. Hog-An­geloni, Don­ald J. Collins, An­dré Jäger, Mi­chael Ka­povich, Akio Kawau­chi, Ul­rich Kos­chorke, Elena Kudryavt­seva, Da­ciberg L. Gonçalves, Maria Her­mínia de Paula Leite Mello, Mar­tin Lust­ig, S. Matveev, Mat­tia Mec­chia, To­motada Oht­suki, Lu­isa Paoluzzi, Joan Porti, Le­onid Potya­gailo, Mar­tin R. Brid­son, Robert Ri­ley, Makoto Sak­uma, Mar­tin Schar­le­mann, Wil­helm Sing­hof, Juan Souto, Kon­stantin Svi­ridov, Satoshi To­moda, Alina Vdov­ina, Ern­est Vin­berg, El­mar Vo­gt, Shicheng Wang, Richard Weidmann, Hein­er Zi­eschang, Bruno Zi­m­mer­mann, Peter Zven­growski.

Pricing and Sales  
logo for open access

Groups, homotopy and configuration spaces (Tokyo, 2005) OA

Norio Iwase, Toshitake Kohno, Ran Levi, Dai Tamaki and Jie Wu (editors)
GTM 13 (2008) xii+546
msp.​org/​gtm/​2008/​13  
cover for Groups, homotopy and configuration spaces <q>(Tokyo, 2005)</q>

This volume is the pro­ceed­ings of the con­fer­ence “Groups, Ho­mo­topy and Con­fig­ur­a­tion Spaces” held at the Uni­versity of Tokyo, Ju­ly 5–11, 2005, in hon­or of the 60th birth­day of Fred Co­hen. The em­phas­is of the con­fer­ence was on co­homo­logy of groups, clas­sic­al and mod­ern ho­mo­topy the­ory, geo­metry and to­po­logy of con­fig­ur­a­tion spaces and re­lated top­ics. However, the con­fer­ence was in­ten­ded to have a broad scope, with talks on a vari­ety of top­ics of cur­rent in­terests in to­po­logy. The or­gan­iz­ing com­mit­tee con­sisted of Norio Iwase, Toshi­take Kohno, Ran Levi, Dai Ta­maki and Jie Wu. The con­fer­ence was sup­por­ted by the COE pro­gram of the Gradu­ate School of Math­em­at­ic­al Sci­ences, The Uni­versity of Tokyo.

Pricing and Sales  
logo for open access

Workshop on Heegaard Splittings (Technion, 2005) OA

Cameron Gordon and Yo'av Moriah (editors)
GTM 12 (2007) xiv+411
msp.​org/​gtm/​2007/​12  
cover for Workshop on Heegaard Splittings <q>(Technion, 2005)</q>

The no­tion of a Hee­gaard split­ting of a 3-man­i­fold is as old as 3-di­men­sion­al to­po­logy it­self; we may re­call, for ex­ample, that Poin­caré de­scribed his do­deca­hed­ral space by means of a Hee­gaard dia­gram. It also seems to be the case that one of the early mo­tiv­a­tions for the study of auto­morph­isms of sur­faces was the de­sire to un­der­stand 3-man­i­folds through their Hee­gaard split­tings. Nev­er­the­less, for many years know­ledge about Hee­gaard split­tings was lim­ited; the fol­low­ing is a more or less com­plete list of things that were known up to 1970: 3-man­i­folds are tri­an­gulable, and hence pos­sess Hee­gaard split­tings (Moise, 1952); any two Hee­gaard split­tings of a giv­en 3-man­i­fold be­come iso­top­ic afer some num­ber of sta­bil­iz­a­tions (Re­idemeister, Sing­er, 1933); S3 has a unique split­ting of any genus up to iso­topy (Wald­hausen, 1968); Hee­gaard genus is ad­dit­ive un­der con­nec­ted sum (Haken, 1968); the al­geb­ra­ic char­ac­ter­iz­a­tion of Hee­gaard split­tings in terms of split­ting ho­mo­morph­isms (Stallings, 1966).

Start­ing in the 1980s, pro­gress in the sub­ject began to ac­cel­er­ate and it entered more and more in­to the main­stream of 3-di­men­sion­al to­po­logy, with de­vel­op­ments com­ing from sev­er­al dif­fer­ent dir­ec­tions. There are now enough gen­er­al res­ults and tech­niques es­tab­lished to jus­ti­fy speak­ing of the the­ory of Hee­gaard split­tings. A (cer­tainly in­com­plete) list of re­cent ad­vances in the sub­ject is the fol­low­ing: the clas­si­fic­a­tion of Hee­gaard split­tings of Seifert fiber spaces; the no­tion of strong ir­re­du­cib­il­ity; the in­tro­duc­tion of the curve com­plex in­to the study of Hee­gaard split­tings; the use of nor­mal and al­most nor­mal sur­faces; res­ults ob­tained us­ing Cerf the­ory (sweep-outs); the ap­plic­a­tion of the the­ory of min­im­al sur­faces; geo­met­ric to­po­lo­gic­al meth­ods, in­clud­ing the the­ory of lam­in­a­tions; res­ults re­lat­ing Hee­gaard split­tings to hy­per­bol­ic struc­tures, for in­stance hy­per­bol­ic volume; res­ults on the tun­nel num­ber of knots; the use of Hee­gaard split­tings to define Hee­gaard–Flo­er ho­mo­logy.

It was against this back­ground that the Tech­nion Work­shop on Hee­gaard Split­tings was held in the sum­mer of 2005. The goal was to gath­er people with a spe­cif­ic in­terest in Hee­gaard split­tings in one work­shop where the state of the art could be ex­posed and dis­cussed.

It was de­cided by the par­ti­cipants to pub­lish a pro­ceed­ings of the work­shop with the hope of mak­ing avail­able to in­ter­ested people a con­cen­trated source of in­form­a­tion about the cur­rent state of re­search on Hee­gaard split­tings. Some pa­pers were so­li­cited from non-par­ti­cipants whose in­terests are close to the field. We wish to thank all those who con­trib­uted to this volume for their ef­forts.

The volume also con­tains a list of prob­lems about Hee­gaard split­tings, con­trib­uted by some of the work­shop par­ti­cipants.

Pricing and Sales  
logo for open access

Proceedings of the School and Conference in Algebraic Topology (Hà Nôi, 2004) OA

John Hubbuck, Nguyen H. V. Hung and Lionel Schwartz (editors)
GTM 11 (2007) vi+441
msp.​org/​gtm/​2007/​11  
cover for Proceedings of the School and Conference in Algebraic Topology <q>(Hà Nôi, 2004)</q>

The Pro­ceed­ings of the in­ter­na­tion­al School and Con­fer­ence in Al­geb­ra­ic To­po­logy, Hà Nội 2004, is a col­lec­tion of art­icles in hon­our of Huỳnh Mùi, the founder of the Vi­et­nam school in Al­geb­ra­ic To­po­logy.

Not long ago, Hà Nội, the cap­it­al city, was known as the cent­ral icon of the long and ter­rible Vi­et­nam War. Nowadays, Hà Nội is proud to be known as a young centre of math­em­at­ics. The in­ter­na­tion­al School and Con­fer­ence in Al­geb­ra­ic To­po­logy, Hà Nội 2004, was the first not­able meet­ing on Al­geb­ra­ic To­po­logy in Vi­et­nam with the par­ti­cip­a­tion of an im­press­ive num­ber of both young and in­ter­na­tion­ally es­tab­lished Al­geb­ra­ic To­po­lo­gists.

The Hà Nội 2004 Pro­ceed­ings’ main top­ics are the Steen­rod al­gebra, in­vari­ant the­ory, clas­si­fy­ing spaces, and group co­homo­logy. It con­tains tran­scripts of some of the school courses and the con­fer­ence talks as well as re­lated art­icles sub­mit­ted spe­cific­ally for the Pro­ceed­ings. Most of the art­icles in the Pro­ceed­ings present ori­gin­al re­search with proofs. Oth­ers are sur­vey art­icles writ­ten by lead­ing ex­perts.

Pricing and Sales  
logo for open access

Proceedings of the Nishida Fest (Kinosaki, 2003) OA

Matthew Ando, Norihiko Minami, Jack Morava and W. Stephen Wilson (editors)
GTM 10 (2007) 449
msp.​org/​gtm/​2007/​10  
cover for Proceedings of the Nishida Fest <q>(Kinosaki, 2003)</q>

A ma­jor in­ter­na­tion­al meet­ing on ho­mo­topy the­ory took place in Kino­saki, Ja­pan, from Ju­ly 28–Au­gust 1 2003, fol­lowed on Au­gust 4–8 by an in­tense satel­lite con­fer­ence at the Nagoya In­sti­tute of Tech­no­logy. This volume con­tains the Pro­ceed­ings of those con­fer­ences. They, and this volume, are ded­ic­ated to Pro­fess­or Gôrô Nishida on the oc­ca­sion of his 60th birth­day.

Nishida’s earli­est work grew out of the study of in­fin­ite loopspaces. His first pa­per (in 1968, on what came even­tu­ally to be known as the Nishida re­la­tions) ac­counts for in­ter­ac­tions between Steen­rod and Dyer–Lashof (Kudo–Araki) op­er­a­tions. This was fol­lowed by early work with H. Toda on the ex­ten­ded power con­struc­tion, which led in 1973 to his mile­stone proof of the nil­po­tence of pos­it­ive-de­gree ele­ments in the stable ho­mo­topy ring of spheres.

This res­ult, whose echoes con­tin­ue to re­ver­ber­ate today in work of Dev­in­atz, Hop­kins, Smith, and oth­ers on the chro­mat­ic pic­ture, and in work on motives in al­geb­ra­ic geo­metry, stood at the time as an isol­ated beacon of hope in the (then very mys­ter­i­ous) world of stable ho­mo­topy the­ory. It, to­geth­er with the Kahn–Priddy the­or­em, was one of the first signs that the sub­ject pos­sesses deep glob­al prop­er­ties—that it held struc­tur­al secrets well bey­ond its already for­mid­able com­pu­ta­tion­al as­pects. Nishida next turned his at­ten­tion to a circle of ideas sur­round­ing the Segal con­jec­ture, trans­fer ho­mo­morph­isms, and stable split­tings of clas­si­fy­ing spaces of groups. The ideas in this series of pa­pers have by now grown in­to a rich sub­field of ho­mo­topy the­ory, with im­port­ant con­tri­bu­tions by Ben­son, Fesh­bach, Mar­tino, Mi­n­ami, Priddy, Webb, and many oth­ers; it con­tin­ues today in (for ex­ample) the the­ory of p-com­pact groups. In re­cent years much of his work has been con­cerned with vari­ous as­pects of el­lipt­ic co­homo­logy. His deep in­sight from the early 90s, that work of Eichler and Shimura on mod­u­lar forms, high­er S1-trans­fers, and the dif­feo­morph­ism group of the two-tor­us are all in­tim­ately con­nec­ted, is still not ad­equately un­der­stood; its ex­ploit­a­tion may de­pend on new geo­met­ric ideas from the de­vel­op­ing the­ory of el­lipt­ic ob­jects.

Pricing and Sales  
logo for open access

Exotic homology manifolds (Oberwolfach, 2003) OA

Frank Quinn and Andrew Ranicki (editors)
GTM 9 (2006) 153
msp.​org/​gtm/​2006/​09  
cover for Exotic homology manifolds <q>(Oberwolfach, 2003)</q>

The Work­shop on Exot­ic Ho­mo­logy Man­i­folds took place at MFO (Math­em­at­isches Forschungsin­sti­tut Ober­wolfach) in Ger­many on June 29th – Ju­ly 5th, 2003.

Ho­mo­logy man­i­folds were de­veloped in the first half of the 20th cen­tury to give a pre­cise set­ting for Poin­caré’s ideas on du­al­ity. Ma­jor res­ults in the second half of the cen­tury came from two dif­fer­ent areas. Meth­ods from the point-set tra­di­tion were used to study ho­mo­logy man­i­folds ob­tained by di­vid­ing genu­ine man­i­folds by fam­il­ies of con­tract­ible sub­sets. Exot­ic ho­mo­logy man­i­folds are ones that can­not be ob­tained in this way, and these have been in­vest­ig­ated us­ing al­geb­ra­ic and geo­met­ric meth­ods. The Mini-Work­shop brought to­geth­er ex­perts from both point-set and al­geb­ra­ic areas, along with new PhDs and ex­perts in re­lated areas. This was the first time this was done in a meet­ing fo­cused only on ho­mo­logy man­i­folds. The 17 par­ti­cipants had 14 form­al lec­tures and a prob­lem ses­sion. There was a par­tic­u­lar fo­cus on the proof, 10 years ago, of the ex­ist­ence of exot­ic ho­mo­logy man­i­folds. This gave ex­perts in each area an the op­por­tun­ity to learn more about de­tails com­ing from the oth­er area. There had also been con­cerns about the cor­rect­ness of one of the lem­mas, and this was dis­cussed in de­tail. One of the high points of the con­fer­ence was the dis­cov­ery of a short and beau­ti­ful new proof of this lemma. Ex­tens­ive dis­cus­sions of ex­amples and prob­lems have un­doubtedly helped pre­pare for fu­ture pro­gress in the field.

These pro­ceed­ings for the meet­ing in­clude an art­icle on the his­tory of the sub­ject and a prob­lem list.

There was also a won­der­ful in­ter­ac­tion with the Mini-Work­shop Henri Poin­caré and to­po­logy, which was held in the same week. There was a joint dis­cus­sion on the early his­tory of man­i­folds, and both groups offered even­ing lec­tures on top­ics of in­terest to the oth­er. Sev­er­al of the day­time his­tory lec­tures also drew large num­bers of ho­mo­logy man­i­fold par­ti­cipants.

Pricing and Sales  
logo for open access

The interaction of finite-type and Gromov–Witten invariants (Banff, 2003) OA

David Auckly and Jim Bryan (editors)
GTM 8 (2006) 456
msp.​org/​gtm/​2006/​08  
cover for The interaction of finite-type and Gromov–Witten invariants <q>(Banff, 2003)</q>

In the sum­mer of 2001, we (Dave and Jim) were at the Gökova con­fer­ence in Tur­key talk­ing about BIRS, the new math­em­at­ics in­sti­tute that was go­ing to open in Ban­ff, Canada, in 2003. Al­though 2003 seemed like a long way off at the time, we wanted to pro­pose a work­shop. For­tu­it­ously, Jim had re­cently heard about some ex­cit­ing work in phys­ics by Go­pak­u­mar, Vafa and oth­ers that had found some very ex­pli­cit con­nec­tions between to­po­lo­gic­al string the­ory and Chern–Si­mons gauge the­ory—the very same phys­ic­al the­or­ies that led to the math­em­at­ic­al the­or­ies of Gro­mov–Wit­ten in­vari­ants and fi­nite type in­vari­ants. Al­though these ideas had not yet taken hold in the math com­munity, it seemed likely that with­in a few years they would be timely and war­rant a work­shop.

In­deed, by 2003, the top­ic was very timely. Phys­i­cists Aganagic, Klemm, Marino, and Vafa had de­veloped the “to­po­lo­gic­al ver­tex”, a gad­get which (con­jec­tur­ally) com­puted Gro­mov–Wit­ten of tor­ic Calabi–Yau threefolds in terms of cer­tain in­vari­ants of fi­nite type: Chern–Si­mons in­vari­ants. Math­em­aticians Li, Liu, Liu, and Zhou had be­gun to de­vel­op a math­em­at­ic­al frame­work for the to­po­lo­gic­al ver­tex. Garoufal­id­is and Le had just proven the LMOV con­jec­ture. This con­jec­ture en­coded in­teg­ral­ity prop­er­ties of the HOM­FLY(PT) poly­no­mi­al that must hold if the con­jec­tur­al large-N du­al­ity was in­deed true. In ad­di­tion new con­jec­tures re­lat­ing large N du­al­ity with Khovan­ov ho­mo­logy were form­ing.

Pricing and Sales  
logo for open access

Proceedings of the Casson Fest (Arkansas and Texas, 2003) OA

Cameron Gordon and Yoav Rieck (editors)
GTM 7 (2004) xii+547
msp.​org/​gtm/​2004/​07  
cover for Proceedings of the Casson Fest <q>(Arkansas and Texas, 2003)</q>

This volume con­tains pa­pers on a wide range of top­ics in low-di­men­sion­al to­po­logy. It arose out of two events that were held in 2003. The first was the 28th Uni­versity of Arkan­sas Spring Lec­ture Series in the Math­em­at­ic­al Sci­ences, which took place April 10–12, 2003. These an­nu­al con­fer­ences fo­cus on a spe­cif­ic top­ic of cur­rent in­terest in math­em­at­ics, and fea­ture a prin­cip­al lec­turer who gives a series of five lec­tures and se­lects ad­di­tion­al in­vited speak­ers. In 2003 the prin­cip­al lec­turer was An­drew Cas­son, and the title of his lec­ture series was "The An­drews-Curtis and the Poin­care Con­jec­tures". The in­vited speak­ers were Steph­en Bi­gelow, Mar­tin Brid­son, Danny Calegari, Nath­an Dun­field, Camer­on Gor­don, Alan Re­id, Mar­tin Schar­le­mann, Zlil Sela, and Peter Shalen. A spe­cial pub­lic lec­ture was giv­en by Jeff Weeks. There were also sev­er­al con­trib­uted talks. The or­gan­izers were Chaim Good­man-Strauss and Yo'av Rieck. The con­fer­ence was sup­por­ted by NSF Grant DMS-0245047 and by the De­part­ment of Math­em­at­ic­al Sci­ences, Ful­bright Col­lege of Arts and Sci­ences and Gradu­ate School of the Uni­versity of Arkan­sas.

The second event was the Con­fer­ence on the To­po­logy of Man­i­folds of Di­men­sions 3 and 4, held at the Uni­versity of Texas at Aus­tin, May 19–21, 2003, in hon­or of the 60th birth­day of An­drew Cas­son. In­vited lec­tures were giv­en by Danny Calegari, Bob Ed­wards, Mike Freed­man, Dave Gabai, Rob Kirby, Greg Ku­per­berg, Dar­ren Long, Peter Oz­s­vath, An­drew Ran­icki, Ron Stern, Peter Teich­ner, Kev­in Walk­er, and Terry Wall. The or­gan­iz­ing com­mit­tee con­sisted of Camer­on Gor­don, Bob Gom­pf, John Luecke and Alan Re­id. The con­fer­ence was sup­por­ted by NSF Grant DMS-0229035 and by the De­part­ment of Math­em­at­ics of the Uni­versity of Texas at Aus­tin.

Pricing and Sales  
logo for open access

Four-manifolds, geometries and knots OA

Jonathan Hillman
GTM 5 (2002) 382
msp.​org/​gtm/​2002/​05  

The goal of this book is to char­ac­ter­ize al­geb­ra­ic­ally the closed 4-man­i­folds that fibre non­trivi­ally or ad­mit geo­met­ries in the sense of Thur­ston, or which are ob­tained by sur­gery on 2-knots, and to provide a ref­er­ence for the to­po­logy of such man­i­folds and knots. The first chapter is purely al­geb­ra­ic. The rest of the book may be di­vided in­to three parts: gen­er­al res­ults on ho­mo­topy and sur­gery (Chapters 2–6), geo­met­ries and geo­met­ric de­com­pos­i­tions (Chapters 7–13), and 2-knots (Chapters 14–18). In many cases the Euler char­ac­ter­ist­ic, fun­da­ment­al group and Stiefel–Whit­ney classes to­geth­er form a com­plete sys­tem of in­vari­ants for the ho­mo­topy type of such man­i­folds, and the pos­sible val­ues of the in­vari­ants can be de­scribed ex­pli­citly. The strongest res­ults are char­ac­ter­iz­a­tions of man­i­folds which fibre ho­mo­top­ic­ally over S1 or an as­pher­ic­al sur­face (up to ho­mo­topy equi­val­ence) and in­fra­solv­man­i­folds (up to homeo­morph­ism). As a con­sequence 2-knots whose groups are poly–Z are de­term­ined up to Gluck re­con­struc­tion and change of ori­ent­a­tions by their groups alone.

This book arose out of two earli­er books: 2-Knots and their Groups and The Al­geb­ra­ic Char­ac­ter­iz­a­tion of Geo­met­ric 4-Man­i­folds, pub­lished by Cam­bridge Uni­versity Press for the Aus­trali­an Math­em­at­ic­al So­ci­ety and for the Lon­don Math­em­at­ic­al So­ci­ety, re­spect­ively. About a quarter of the present text has been taken from these books, and I thank Cam­bridge Uni­versity Press for their per­mis­sion to use this ma­ter­i­al. The ar­gu­ments have been im­proved and the res­ults strengthened, not­ably in us­ing Bowditch’s ho­mo­lo­gic­al cri­terion for vir­tu­al sur­face groups to stream­line the res­ults on sur­face bundles, us­ing L2 meth­ods in­stead of loc­al­iz­a­tion, com­plet­ing the char­ac­ter­iz­a­tion of map­ping tori, re­lax­ing the hy­po­theses on tor­sion or on abeli­an nor­mal sub­groups in the fun­da­ment­al group and in de­riv­ing the res­ults on 2–knot groups from the work on 4–man­i­folds. The main tools used are co­homo­logy of groups, equivari­ant Poin­care du­al­ity and (to a less­er ex­tent) L2–co­homo­logy, 3–man­i­fold the­ory and sur­gery.

The book has been re­vised in March 2007.

Jonath­an Hill­man

Pricing and Sales  
logo for open access

Invariants of knots and 3-manifolds (Kyoto, 2001) OA

T. Ohtsuki, T. Kohno, T. Le, J. Murakami, J. Roberts and V. Turaev (editors)
GTM 4 (2002) 572
msp.​org/​gtm/​2002/​04  

The work­shop and sem­inars on “In­vari­ants of Knots and 3-Man­i­folds” took place at the Re­search In­sti­tute for Math­em­at­ic­al Sci­ences (RIMS), Kyoto Uni­versity, in Septem­ber 2001. The work­shop was held over the peri­od Septem­ber 17–21. Sem­inars were held on the Tues­days, Wed­nes­days and Thursdays of the oth­er weeks of Septem­ber, in­clud­ing “Gous­sarov day” on Septem­ber 25.

Since the in­ter­ac­tion between geo­metry and math­em­at­ic­al phys­ics in the 1980s, many in­vari­ants of knots and 3-man­i­folds have been dis­covered and stud­ied: poly­no­mi­al in­vari­ants such as the Jones poly­no­mi­al, Vassiliev in­vari­ants, the Kont­sevich in­vari­ant of knots, quantum and per­turb­at­ive in­vari­ants, the LMO in­vari­ant and fi­nite type in­vari­ants of 3-man­i­folds. The dis­cov­ery and ana­lys­is of the enorm­ous num­ber of these in­vari­ants yiel­ded a new area: the study of in­vari­ants of knots and 3-man­i­folds (from an­oth­er view­point, the study of the sets of knots and 3-man­i­folds). There are also de­vel­op­ing top­ics re­lated to oth­er areas such as hy­per­bol­ic geo­metry via the volume con­jec­ture and the the­ory of op­er­at­or al­geb­ras via in­vari­ants arising from 6j-sym­bols. On the oth­er hand, re­cent works have al­most com­pleted the to­po­lo­gic­al re­con­struc­tion of the in­vari­ants de­rived from the Chern-Si­mons field the­ory.

An aim of the work­shop and sem­inars was to dis­cuss fu­ture dir­ec­tions for this area. To dis­cuss these mat­ters fully, we planned one month of activ­it­ies, re­l­at­ively longer than usu­al. Fur­ther, to en­cour­age dis­cus­sions among the par­ti­cipants, we ar­ranged a short prob­lem ses­sion after each talk, and re­ques­ted the speak­er to give his/her open prob­lems there. Many in­ter­est­ing prob­lems were presen­ted in these prob­lem ses­sions and, based on them, we had valu­able dis­cus­sions in and between sem­inars and the work­shop. Open prob­lems dis­cussed there were ed­ited and formed in­to a prob­lem list, which, I hope, will cla­ri­fy the present fron­ti­er of this area and as­sist read­ers when con­sid­er­ing fu­ture dir­ec­tions.

T. Oht­suki

Pricing and Sales  
logo for open access

Invitation to higher local fields (Münster, 1999) OA

Ivan Fesenko and Masato Kurihara (editors)
GTM 3 (2000) 304
msp.​org/​gtm/​2000/​03  

Temporarily OUT OF PRINT.

This mono­graph is the res­ult of the con­fer­ence on high­er loc­al fields held in Mün­ster, Au­gust 29 to Septem­ber 5, 1999. The aim is to provide an in­tro­duc­tion to high­er loc­al fields (more gen­er­ally com­plete dis­crete valu­ation fields with ar­bit­rary residue field) and render the main ideas of this the­ory (Part I), as well as to dis­cuss sev­er­al ap­plic­a­tions and con­nec­tions to oth­er areas (Part II). The volume grew as an ex­ten­ded ver­sion of talks giv­en at the con­fer­ence. The two parts are sep­ar­ated by a pa­per of K. Kato, an IHES pre­print from 1980 which has nev­er been pub­lished.

An n-di­men­sion­al loc­al field is a com­plete dis­crete valu­ation field whose residue field is an (n–1)-di­men­sion­al loc­al field; 0-di­men­sion­al loc­al fields are just per­fect (e.g., fi­nite) fields of pos­it­ive char­ac­ter­ist­ic. Giv­en an arith­met­ic scheme, there is a high­er loc­al field as­so­ci­ated to a flag of sub­s­chemes on it. One of cent­ral res­ults on high­er loc­al fields, class field the­ory, de­scribes abeli­an ex­ten­sions of an n-di­men­sion­al loc­al field via (all in the case of fi­nite 0-di­men­sion­al residue field; some in the case of in­fin­ite 0-di­men­sion­al residue field) closed sub­groups of the n-th Mil­nor K-group of F.

We hope that the volume will be a use­ful in­tro­duc­tion and guide to the sub­ject. The con­tri­bu­tions to this volume were re­ceived over the peri­od Novem­ber 1999 to Au­gust 2000 and the elec­tron­ic pub­lic­a­tion date is 10 Decem­ber 2000.

Ivan Fesen­ko and Masato Kur­i­hara

logo for open access

Proceedings of the Kirbyfest (Berkeley, 1998) OA

Joel Hass and Martin Scharlemann (editors)
GTM 2 (1999) xvi+581
msp.​org/​gtm/​1999/​02  
cover for Proceedings of the Kirbyfest <q>(Berkeley, 1998)</q>

Temporarily OUT OF PRINT.

Rob Kirby’s re­search spans a broad spec­trum of top­ics, all with this strong visu­al fla­vor: to­po­lo­gic­al man­i­folds of high di­men­sion; the struc­ture of smooth 4-man­i­folds and their re­la­tion­ship to com­plex sur­faces; and the emer­ging new in­vari­ants for both 3- and 4-di­men­sion­al man­i­folds. In both di­men­sions three and four, the “Kirby Cal­cu­lus” has be­come a stand­ard ana­lyt­ic­al tool. He has helped to or­gan­ize and to de­vel­op prob­lem lists which have be­come stand­ard ref­er­ence points for pro­gress in geo­met­ric to­po­logy.

The Kirby­fest, held at the Math­em­at­ic­al Sci­ences Re­search In­sti­tute on 22–26 June 1998, at­trac­ted over 100 math­em­aticians from around the globe. Many of the par­ti­cipants were col­lab­or­at­ors, or former stu­dents; oth­ers were just fans of Kirby and his work. There were 27 plen­ary talks, cov­er­ing a wide vari­ety of to­po­lo­gic­ally re­lated sub­jects, in­clud­ing sev­er­al his­tor­ic­al sur­veys. Fields Medal­ists gave five of the talks. Sev­en present­a­tions were spe­cific­ally or­gan­ized to be eas­ily ac­cess­ible to gradu­ate stu­dents.

We hope these pro­ceed­ings con­vey some of the math­em­at­ic­al ex­cite­ment of the Kirby­fest week, and we are honored to ded­ic­ate it to Rob.

logo for open access

The Epstein birthday schrift OA

Igor Rivin, Colin Rourke and Caroline Series (editors)
GTM 1 (1998) 576
msp.​org/​gtm/​1998/​01  

Temporarily OUT OF PRINT.

In hon­or of Dav­id Ep­stein.