Geometry & Topology Volume 20, issue 2 (2016)

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An algebraic approach to virtual fundamental cycles on moduli spaces of pseudo-holomorphic curves

John Pardon

Geometry & Topology 20 (2016) 779–1034

DOI: 10.2140/gt.2016.20.779

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