Volume 20, issue 2 (2016)

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

Volume 26
Issue 8, 3307–3833
Issue 7, 2855–3306
Issue 6, 2405–2853
Issue 5, 1907–2404
Issue 4, 1435–1905
Issue 3, 937–1434
Issue 2, 477–936
Issue 1, 1–476

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

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
Editorial Interests
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
An algebraic approach to virtual fundamental cycles on moduli spaces of pseudo-holomorphic curves

John Pardon

Geometry & Topology 20 (2016) 779–1034
Bibliography
1 M Abouzaid, Framed bordism and Lagrangian embeddings of exotic spheres, Ann. of Math. 175 (2012) 71 MR2874640
2 M Abouzaid, Nearby Lagrangians with vanishing Maslov class are homotopy equivalent, Invent. Math. 189 (2012) 251 MR2947545
3 J F Adams, On the cobar construction, Proc. Nat. Acad. Sci. U.S.A. 42 (1956) 409 MR0079266
4 F J Almgren Jr., The homotopy groups of the integral cycle groups, Topology 1 (1962) 257 MR0146835
5 M F Atiyah, I G Macdonald, Introduction to commutative algebra, Addison-Wesley (1969) MR0242802
6 J F Barraud, O Cornea, Lagrangian intersections and the Serre spectral sequence, Ann. of Math. 166 (2007) 657 MR2373371
7 N A Berikashvili, The Steenrod–Sitnikov homology theory on the category of compact spaces, Dokl. Akad. Nauk SSSR 254 (1980) 1289 MR592491
8 N A Berikashvili, Axiomatics of the Steenrod–Sitnikov homology theory on the category of compact Hausdorff spaces, Trudy Mat. Inst. Steklov. 154 (1983) 24 MR733823
9 R H Bing, The cartesian product of a certain nonmanifold and a line is E4, Ann. of Math. 70 (1959) 399 MR0107228
10 D Borisov, J Noel, Simplicial approach to derived differential manifolds, preprint (2011) arXiv:1112.0033
11 J W Cannon, Shrinking cell-like decompositions of manifolds: codimension three, Ann. of Math. 110 (1979) 83 MR541330
12 G Carlsson, E K Pedersen, Čech homology and the Novikov conjectures for K– and L–theory, Math. Scand. 82 (1998) 5 MR1634649
13 G S Chogoshvili, On the equivalence of the functional and spectral theory of homology, Izvestiya Akad. Nauk SSSR. Ser. Mat. 15 (1951) 421 MR0046649
14 R L Cohen, J D S Jones, G B Segal, Floer’s infinite-dimensional Morse theory and homotopy theory, from: "The Floer memorial volume" (editors H Hofer, C H Taubes, A Weinstein, E Zehnder), Progr. Math. 133, Birkhäuser (1995) 297 MR1362832
15 C C Conley, E Zehnder, The Birkhoff–Lewis fixed point theorem and a conjecture of V I Arnol’d, Invent. Math. 73 (1983) 33 MR707347
16 M Damian, On the stable Morse number of a closed manifold, Bull. London Math. Soc. 34 (2002) 420 MR1897421
17 A Dress, Zur Spectralsequenz von Faserungen, Invent. Math. 3 (1967) 172 MR0267585
18 D A Edwards, H M Hastings, Čech and Steenrod homotopy theories with applications to geometric topology, 542, Springer (1976) MR0428322
19 T Ekholm, I Smith, Exact Lagrangian immersions with one double point revisited, Math. Ann. 358 (2014) 195 MR3157996
20 T Ekholm, I Smith, Exact Lagrangian immersions with a single double point, J. Amer. Math. Soc. 29 (2016) 1 MR3402693
21 Y Eliashberg, Estimates on the number of fixed points of area preserving transformations, preprint (1979)
22 A Floer, A relative Morse index for the symplectic action, Comm. Pure Appl. Math. 41 (1988) 393 MR933228
23 A Floer, The unregularized gradient flow of the symplectic action, Comm. Pure Appl. Math. 41 (1988) 775 MR948771
24 A Floer, Symplectic fixed points and holomorphic spheres, Comm. Math. Phys. 120 (1989) 575 MR987770
25 A Floer, H Hofer, Coherent orientations for periodic orbit problems in symplectic geometry, Math. Z. 212 (1993) 13 MR1200162
26 A Floer, H Hofer, K Wysocki, Applications of symplectic homology, I, Math. Z. 217 (1994) 577 MR1306027
27 E M Friedlander, Étale homotopy of simplicial schemes, 104, Princeton Univ. Press (1982) MR676809
28 K Fukaya, The symplectic s–cobordism conjecture : a summary, from: "Geometry and physics" (editors J E Andersen, J Dupont, H Pedersen, A Swann), Lecture Notes in Pure and Appl. Math. 184, Dekker (1997) 209 MR1423167
29 K Fukaya, Y G Oh, H Ohta, K Ono, Lagrangian intersection Floer theory : Anomaly and obstruction, I, 46, Amer. Math. Soc. (2009) MR2553465
30 K Fukaya, Y G Oh, H Ohta, K Ono, Lagrangian intersection Floer theory : Anomaly and obstruction, II, 46, Amer. Math. Soc. (2009) MR2548482
31 K Fukaya, Y G Oh, H Ohta, K Ono, Technical details on Kuranishi structure and virtual fundamental chain, preprint (2012) arXiv:1209.4410
32 K Fukaya, Y G Oh, H Ohta, K Ono, Kuranishi structure, pseudo-holomorphic curve, and virtual fundamental chain, Part 1, preprint (2015) arXiv:1503.07631
33 K Fukaya, K Ono, Arnold conjecture and Gromov–Witten invariant, Topology 38 (1999) 933 MR1688434
34 R Godement, Topologie algébrique et théorie des faisceaux, 1252, Hermann (1958) MR0102797
35 B Goldfarb, Novikov conjectures for arithmetic groups with large actions at infinity, K-Theory 11 (1997) 319 MR1451760
36 M Gromov, Pseudoholomorphic curves in symplectic manifolds, Invent. Math. 82 (1985) 307 MR809718
37 M Gromov, Singularities, expanders and topology of maps, Part 2 : From combinatorics to topology via algebraic isoperimetry, Geom. Funct. Anal. 20 (2010) 416 MR2671284
38 H M Hastings, Steenrod homotopy theory, homotopy idempotents, and homotopy limits, from: "Proceedings of the 1977 Topology Conference, II" (editors W Kuperberg, G M Reed, P Zenor), Topology Proc. 2 (1977) 461 MR540623
39 A Hatcher, Algebraic topology, Cambridge Univ. Press (2002) MR1867354
40 H Hofer, D A Salamon, Floer homology and Novikov rings, from: "The Floer memorial volume" (editors H Hofer, C H Taubes, A Weinstein, E Zehnder), Progr. Math. 133, Birkhäuser (1995) 483 MR1362838
41 H Hofer, K Wysocki, E Zehnder, A general Fredholm theory, I : A splicing-based differential geometry, J. Eur. Math. Soc. (JEMS) 9 (2007) 841 MR2341834
42 H Hofer, K Wysocki, E Zehnder, A general Fredholm theory, II : Implicit function theorems, Geom. Funct. Anal. 19 (2009) 206 MR2507223
43 H Hofer, K Wysocki, E Zehnder, A general Fredholm theory, III : Fredholm functors and polyfolds, Geom. Topol. 13 (2009) 2279 MR2515707
44 H Hofer, K Wysocki, E Zehnder, Integration theory on the zero sets of polyfold Fredholm sections, Math. Ann. 346 (2010) 139 MR2558891
45 H Hofer, K Wysocki, E Zehnder, sc-smoothness, retractions and new models for smooth spaces, Discrete Contin. Dyn. Syst. 28 (2010) 665 MR2644764
46 H Hofer, K Wysocki, E Zehnder, Applications of polyfold theory, I : The polyfolds of Gromov–Witten theory, preprint (2014) arXiv:1107.2097
47 H Hofer, K Wysocki, E Zehnder, Polyfold and Fredholm theory, I : Basic theory in M–polyfolds, preprint (2014) arXiv:1407.3185
48 H Inassaridze, On the Steenrod homology theory of compact spaces, Michigan Math. J. 38 (1991) 323 MR1116492
49 D Joyce, D-manifolds and d-orbifolds: a theory of derived differential geometry, Book manuscript (2012)
50 D Joyce, An introduction to d-manifolds and derived differential geometry, from: "Moduli spaces" (editor Cambridge), London Math. Soc. Lecture Note Ser. 411, Cambridge Univ. Press (2014) 230 MR3221297
51 M Kontsevich, Enumeration of rational curves via torus actions, from: "The moduli space of curves" (editors R Dijkgraaf, C Faber, G van der Geer), Progr. Math. 129, Birkhäuser (1995) 335 MR1363062
52 M Kontsevich, Y Manin, Gromov–Witten classes, quantum cohomology, and enumerative geometry, Comm. Math. Phys. 164 (1994) 525 MR1291244
53 J Li, G Tian, Virtual moduli cycles and Gromov–Witten invariants of general symplectic manifolds, from: "Topics in symplectic 4–manifolds" (editor R J Stern), First Int. Press Lect. Ser. 1, Int. Press (1998) 47 MR1635695
54 G Liu, G Tian, Floer homology and Arnold conjecture, J. Differential Geom. 49 (1998) 1 MR1642105
55 R B Lockhart, R C McOwen, Elliptic differential operators on noncompact manifolds, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 12 (1985) 409 MR837256
56 G Lu, G Tian, Constructing virtual Euler cycles and classes, Int. Math. Res. Surv. 2007 (2007) MR2369606
57 J Lurie, Higher topos theory, (2012)
58 J Lurie, Higher algebra, (2014)
59 S Mardešić, Strong shape and homology, Springer (2000) MR1740831
60 D McDuff, Notes on Kuranishi atlases, preprint (2015) arXiv:1411.4306v2
61 D McDuff, D Salamon, J–holomorphic curves and quantum cohomology, 6, Amer. Math. Soc. (1994) MR1286255
62 D McDuff, D Salamon, J–holomorphic curves and symplectic topology, 52, Amer. Math. Soc. (2004) MR2045629
63 D McDuff, K Wehrheim, Kuranishi atlases with trivial isotropy, preprint (2015) arXiv:1208.1340v6
64 J Milnor, On the Steenrod homology theory, from: "Novikov conjectures, index theorems and rigidity, Vol. 1" (editors S C Ferry, A Ranicki, J Rosenberg), London Math. Soc. Lecture Note Ser. 226, Cambridge Univ. Press (1995) 79 MR1388297
65 M P Muller, Gromov’s Schwarz lemma as an estimate of the gradient for holomorphic curves, from: "Holomorphic curves in symplectic geometry" (editors M Audin, J Lafontaine), Progr. Math. 117, Birkhäuser (1994) 217 MR1274931
66 K Ono, On the Arnol’d conjecture for weakly monotone symplectic manifolds, Invent. Math. 119 (1995) 519 MR1317649
67 M S Osborne, Basic homological algebra, 196, Springer (2000) MR1757274
68 J Pardon, The Hilbert–Smith conjecture for three-manifolds, J. Amer. Math. Soc. 26 (2013) 879 MR3037790
69 S Piunikhin, D Salamon, M Schwarz, Symplectic Floer–Donaldson theory and quantum cohomology, from: "Contact and symplectic geometry" (editor C B Thomas), Publ. Newton Inst. 8, Cambridge Univ. Press (1996) 171 MR1432464
70 J J Rotman, An introduction to homological algebra, Springer (2009)
71 Y Ruan, Virtual neighborhoods and pseudo-holomorphic curves, from: "Proceedings of 6th Gökova Geometry-Topology Conference", Turkish J. Math. 23 (1999) 161 MR1701645
72 D Salamon, Lectures on Floer homology, from: "Symplectic geometry and topology" (editors Y Eliashberg, L Traynor), IAS/Park City Math. Ser. 7, Amer. Math. Soc. (1999) 143 MR1702944
73 D Salamon, E Zehnder, Morse theory for periodic solutions of Hamiltonian systems and the Maslov index, Comm. Pure Appl. Math. 45 (1992) 1303 MR1181727
74 N Spaltenstein, Resolutions of unbounded complexes, Compositio Math. 65 (1988) 121 MR932640
75 D I Spivak, Derived smooth manifolds, Duke Math. J. 153 (2010) 55 MR2641940
76 N E Steenrod, Regular cycles of compact metric spaces, Ann. of Math. 41 (1940) 833 MR0002544
77 M G Sullivan, K–theoretic invariants for Floer homology, Geom. Funct. Anal. 12 (2002) 810 MR1935550
78 W P Thurston, The geometry and topology of three-manifolds, lecture notes (1979)
79 K Wehrheim, Energy quantization and mean value inequalities for nonlinear boundary value problems, J. Eur. Math. Soc. 7 (2005) 305 MR2156603
80 K Wehrheim, Smooth structures on Morse trajectory spaces, featuring finite ends and associative gluing, from: "Proceedings of the Freedman Fest" (editors R Kirby, V Krushkal, Z Wang), Geom. Topol. Monogr. 18 (2012) 369 MR3084244