Volume 22, issue 5 (2018)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 23
Issue 5, 2165–2700
Issue 4, 1621–2164
Issue 3, 1085–1619
Issue 2, 541–1084
Issue 1, 1–540

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Subscriptions
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
Alexander and Thurston norms, and the Bieri–Neumann–Strebel invariants for free-by-cyclic groups

Florian Funke and Dawid Kielak

Geometry & Topology 22 (2018) 2647–2696
Bibliography
1 J W Alexander, Topological invariants of knots and links, Trans. Amer. Math. Soc. 30 (1928) 275 MR1501429
2 L Bartholdi, Amenability of groups is characterized by Myhill’s theorem, with an appendix by D Kielak, preprint (2016) arXiv:1605.09133
3 M Bestvina, M Feighn, M Handel, The Tits alternative for Out(Fn), I : Dynamics of exponentially-growing automorphisms, Ann. of Math. 151 (2000) 517 MR1765705
4 R Bieri, W D Neumann, R Strebel, A geometric invariant of discrete groups, Invent. Math. 90 (1987) 451 MR914846
5 C H Cashen, G Levitt, Mapping tori of free group automorphisms, and the Bieri–Neumann–Strebel invariant of graphs of groups, J. Group Theory 19 (2016) 191 MR3466593
6 J C Cha, S Friedl, F Funke, The Grothendieck group of polytopes and norms, Münster J. Math. 10 (2017) 75 MR3624102
7 M Clay, 2–torsion of free-by-cyclic groups, Q. J. Math. 68 (2017) 617 MR3667215
8 P M Cohn, Free ideal rings and localization in general rings, 3, Cambridge Univ. Press (2006) MR2246388
9 W Dicks, P Menal, The group rings that are semifirs, J. London Math. Soc. 19 (1979) 288 MR533328
10 J Dieudonné, Les déterminants sur un corps non commutatif, Bull. Soc. Math. France 71 (1943) 27 MR0012273
11 J Dubois, S Friedl, W Lück, The L2–Alexander torsion of 3–manifolds, preprint (2014) arXiv:1410.6918
12 N M Dunfield, Alexander and Thurston norms of fibered 3–manifolds, Pacific J. Math. 200 (2001) 43 MR1863406
13 R H Fox, Free differential calculus, I : Derivation in the free group ring, Ann. of Math. 57 (1953) 547 MR0053938
14 S Friedl, W Lück, The L2–torsion function and the Thurston norm of 3–manifolds, preprint (2015) arXiv:1510.00264
15 S Friedl, W Lück, L2–Euler characteristics and the Thurston norm, preprint (2016) arXiv:1609.07805
16 S Friedl, W Lück, Universal L2–torsion, polytopes and applications to 3–manifolds, Proc. Lond. Math. Soc. 114 (2017) 1114 MR3661347
17 S Friedl, S Tillmann, Two-generator one-relator groups and marked polytopes, preprint (2015) arXiv:1501.03489
18 F Funke, The integral polytope group, preprint (2016) arXiv:1605.01217
19 F Funke, The L2–torsion polytope of amenable groups, preprint (2017) arXiv:1704.07164
20 R Geoghegan, M L Mihalik, M Sapir, D T Wise, Ascending HNN extensions of finitely generated free groups are Hopfian, Bull. London Math. Soc. 33 (2001) 292 MR1817768
21 M Hall Jr., Subgroups of finite index in free groups, Canadian J. Math. 1 (1949) 187 MR0028836
22 S L Harvey, Higher-order polynomial invariants of 3–manifolds giving lower bounds for the Thurston norm, Topology 44 (2005) 895 MR2153977
23 S L Harvey, Monotonicity of degrees of generalized Alexander polynomials of groups and 3–manifolds, Math. Proc. Cambridge Philos. Soc. 140 (2006) 431 MR2225642
24 S Harvey, S Friedl, Non-commutative multivariable Reidemester torsion and the Thurston norm, Algebr. Geom. Topol. 7 (2007) 755 MR2308963
25 G Higman, The units of group-rings, Proc. London Math. Soc. 46 (1940) 231 MR0002137
26 D H Kochloukova, Some Novikov rings that are von Neumann finite and knot-like groups, Comment. Math. Helv. 81 (2006) 931 MR2271229
27 P Linnell, W Lück, Localization, Whitehead groups, and the Atiyah conjecture, preprint (2016) arXiv:1602.06906
28 W Lück, L2–invariants : theory and applications to geometry and K–theory, 44, Springer (2002) MR1926649
29 W Lück, Twisting L2–invariants with finite-dimensional representations, preprint (2015) arXiv:1510.00057
30 W Lück, T Schick, L2–torsion of hyperbolic manifolds of finite volume, Geom. Funct. Anal. 9 (1999) 518 MR1708444
31 A I Mal’cev, On the embedding of group algebras in division algebras, Doklady Akad. Nauk SSSR 60 (1948) 1499 MR0025457
32 C T McMullen, The Alexander polynomial of a 3–manifold and the Thurston norm on cohomology, Ann. Sci. École Norm. Sup. 35 (2002) 153 MR1914929
33 B H Neumann, On ordered division rings, Trans. Amer. Math. Soc. 66 (1949) 202 MR0032593
34 J C Sikorav, Homologie de Novikov associée à une classe de cohomologie réelle de degré un, Thèse d’Etat, Universit’e Paris-Sud XI, Orsay (1987)
35 J R Silvester, Introduction to algebraic K–theory, Chapman & Hall (1981) MR629979
36 J R Stallings, Topology of finite graphs, Invent. Math. 71 (1983) 551 MR695906
37 R Strebel, Notes on the Sigma invariants, preprint (2012) arXiv:1204.0214
38 D Tamari, A refined classification of semi-groups leading to generalized polynomial rings with a generalized degree concept, from: "Proceedings of the International Congress of Mathematicians" (editors J C H Gerretsen, J d Groot), North-Holland (1957) 439
39 W P Thurston, A norm for the homology of 3–manifolds, Mem. Amer. Math. Soc. 339, Amer. Math. Soc. (1986) 99 MR823443
40 F Waldhausen, Algebraic K–theory of generalized free products, III, IV, Ann. of Math. 108 (1978) 205 MR0498808
41 C Wegner, The Farrell–Jones conjecture for virtually solvable groups, J. Topol. 8 (2015) 975 MR3431666