Geometry & Topology Volume 27, issue 4 (2023)

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Floer theory and reduced cohomology on open manifolds

Yoel Groman

Geometry & Topology 27 (2023) 1273–1390

DOI: 10.2140/gt.2023.27.1273

Bibliography

1	M Abouzaid, A geometric criterion for generating the Fukaya category, Publ. Math. Inst. Hautes Études Sci. 112 (2010) 191 MR2737980
2	M Abouzaid, Framed bordism and Lagrangian embeddings of exotic spheres, Ann. of Math. 175 (2012) 71 MR2874640
3	M Abouzaid, Family Floer cohomology and mirror symmetry, from: "Proceedings of the International Congress of Mathematicians, II" (editors S Y Jang, Y R Kim, D W Lee, I Yie), Kyung Moon Sa (2014) 813 MR3728639
4	M Abouzaid, Symplectic cohomology and Viterbo’s theorem, from: "Free loop spaces in geometry and topology" (editors J Latschev, A Oancea), IRMA Lect. Math. Theor. Phys. 24, Eur. Math. Soc. (2015) 271 MR3444367
5	M Abouzaid, P Seidel, An open string analogue of Viterbo functoriality, Geom. Topol. 14 (2010) 627 MR2602848
6	M Audin, F Lalonde, L Polterovich, Symplectic rigidity : Lagrangian submanifolds, from: "Holomorphic curves in symplectic geometry" (editors M Audin, J Lafontaine), Progr. Math. 117, Birkhäuser (1994) 271 MR1274934
7	D Auroux, Mirror symmetry and T–duality in the complement of an anticanonical divisor, J. Gökova Geom. Topol. 1 (2007) 51 MR2386535
8	D Auroux, Special Lagrangian fibrations, wall-crossing, and mirror symmetry, from: "Surveys in differential geometry, XIII : Geometry, analysis, and algebraic geometry" (editors H D Cao, S T Yau), Surv. Differ. Geom. 13, International (2009) 1 MR2537081
9	S Bosch, Lectures on formal and rigid geometry, 2105, Springer (2014) MR3309387
10	M P do Carmo, Riemannian geometry, Birkhäuser (1992) MR1138207
11	J Cheeger, M Goresky, R MacPherson, L²–cohomology and intersection homology of singular algebraic varieties, from: "Seminar on differential geometry" (editor S T Yau), Ann. of Math. Stud. 102, Princeton Univ. Press (1982) 303 MR645745
12	J Cheeger, M Gromov, M Taylor, Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds, J. Differential Geometry 17 (1982) 15 MR658471
13	Y V Chekanov, Lagrangian intersections, symplectic energy, and areas of holomorphic curves, Duke Math. J. 95 (1998) 213 MR1646550
14	K Cieliebak, Y Eliashberg, From Stein to Weinstein and back : symplectic geometry of affine complex manifolds, 59, Amer. Math. Soc. (2012) MR3012475
15	K Cieliebak, A Floer, H Hofer, Symplectic homology, II : A general construction, Math. Z. 218 (1995) 103 MR1312580
16	K Cieliebak, U Frauenfelder, G P Paternain, Symplectic topology of Mañé’s critical values, Geom. Topol. 14 (2010) 1765 MR2679582
17	K Cieliebak, V L Ginzburg, E Kerman, Symplectic homology and periodic orbits near symplectic submanifolds, Comment. Math. Helv. 79 (2004) 554 MR2081726
18	K Cieliebak, A Oancea, Symplectic homology and the Eilenberg–Steenrod axioms, Algebr. Geom. Topol. 18 (2018) 1953 MR3797062
19	A Daemi, K Fukaya, Monotone Lagrangian Floer theory in smooth divisor complements, II, preprint (2018) arXiv:1809.03409
20	X Dai, An introduction to L² cohomology, from: "Topology of stratified spaces" (editors G Friedman, E Hunsicker, A Libgober, L Maxim), Math. Sci. Res. Inst. Publ. 58, Cambridge Univ. Press (2011) 1 MR2796405
21	S Dostoglou, D A Salamon, Self-dual instantons and holomorphic curves, Ann. of Math. 139 (1994) 581 MR1283871
22	O Fabert, Contact homology of Hamiltonian mapping tori, Comment. Math. Helv. 85 (2010) 203 MR2563686
23	A Floer, H Hofer, D Salamon, Transversality in elliptic Morse theory for the symplectic action, Duke Math. J. 80 (1995) 251 MR1360618
24	S Ganatra, Symplectic cohomology and duality for the wrapped Fukaya category, preprint (2013) arXiv:1304.7312
25	S Ganatra, Cyclic homology, S¹–equivariant Floer cohomology, and Calabi–Yau structures, preprint (2019) arXiv:1912.13510
26	S Ganatra, J Pardon, V Shende, Covariantly functorial wrapped Floer theory on Liouville sectors, Publ. Math. Inst. Hautes Études Sci. 131 (2020) 73 MR4106794
27	R E Greene, H Wu, C^∞ approximations of convex, subharmonic, and plurisubharmonic functions, Ann. Sci. École Norm. Sup. 12 (1979) 47 MR532376
28	P Griffiths, J Harris, Principles of algebraic geometry, Wiley (1978) MR507725
29	Y Groman, The wrapped Fukaya category for semi-toric SYZ fibrations, preprint (2018) arXiv:1805.03635
30	Y Groman, W J Merry, The symplectic cohomology of magnetic cotangent bundles, preprint (2018) arXiv:1809.01085
31	M Gromov, Pseudo holomorphic curves in symplectic manifolds, Invent. Math. 82 (1985) 307 MR809718
32	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
33	J Kang, Symplectic homology of displaceable Liouville domains and leafwise intersection points, Geom. Dedicata 170 (2014) 135 MR3199480
34	H Karcher, Riemannian comparison constructions, from: "Global differential geometry" (editor S S Chern), MAA Stud. Math. 27, Math. Assoc. America (1989) 170 MR1013810
35	G Lu, Virtual moduli cycles and Gromov–Witten invariants of noncompact symplectic manifolds, Comm. Math. Phys. 261 (2006) 43 MR2193206
36	W Lück, L²–invariants : theory and applications to geometry and K–theory, 44, Springer (2002) MR1926649
37	D McDuff, D Salamon, J–holomorphic curves and symplectic topology, 52, Amer. Math. Soc. (2004) MR2045629
38	D McDuff, D Salamon, Introduction to symplectic topology, Oxford Univ. Press (2017) MR3674984
39	J Milnor, Morse theory, 51, Princeton Univ. Press (1963) MR0163331
40	A Nabutovsky, Disconnectedness of sublevel sets of some Riemannian functionals, Geom. Funct. Anal. 6 (1996) 703 MR1406670
41	A Oancea, A survey of Floer homology for manifolds with contact type boundary or symplectic homology, from: "Symplectic geometry and Floer homology : a survey of the Floer homology for manifolds with contact type boundary or symplectic homology", Ensaios Mat. 7, Soc. Brasil. Mat. (2004) 51 MR2100955
42	A Oancea, The Künneth formula in Floer homology for manifolds with restricted contact type boundary, Math. Ann. 334 (2006) 65 MR2208949
43	K Ono, Some remarks on group actions in symplectic geometry, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 35 (1988) 431 MR965009
44	M Pabiniak, Displacing (Lagrangian) submanifolds in the manifolds of full flags, Adv. Geom. 15 (2015) 101 MR3300713
45	P Petersen, Riemannian geometry, 171, Springer (2006) MR2243772
46	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
47	A F Ritter, Deformations of symplectic cohomology and exact Lagrangians in ALE spaces, Geom. Funct. Anal. 20 (2010) 779 MR2720232
48	A F Ritter, Topological quantum field theory structure on symplectic cohomology, J. Topol. 6 (2013) 391 MR3065181
49	A F Ritter, Floer theory for negative line bundles via Gromov–Witten invariants, Adv. Math. 262 (2014) 1035 MR3228449
50	A F Ritter, I Smith, The monotone wrapped Fukaya category and the open-closed string map, Selecta Math. 23 (2017) 533 MR3595902
51	J Robbin, D Salamon, The Maslov index for paths, Topology 32 (1993) 827 MR1241874
52	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
53	P Schneider, Nonarchimedean functional analysis, Springer (2002) MR1869547
54	M Schwarz, Cohomology operations from S¹–cobordisms in Floer homology, PhD thesis, Swiss Federal Institute of Technology Zurich (1995)
55	P Seidel, Fukaya categories and deformations, from: "Proceedings of the International Congress of Mathematicians" (editor T Li), Higher Ed. (2002) 351 MR1957046
56	P Seidel, A biased view of symplectic cohomology, from: "Current developments in mathematics, 2006" (editors B Mazur, T Mrowka, W Schmid, R Stanley, S T Yau), International (2008) 211 MR2459307
57	J C Sikorav, Some properties of holomorphic curves in almost complex manifolds, from: "Holomorphic curves in symplectic geometry" (editors M Audin, J Lafontaine), Progr. Math. 117, Birkhäuser (1994) 165 MR1274929
58	J Tu, On the reconstruction problem in mirror symmetry, Adv. Math. 256 (2014) 449 MR3177298
59	M Usher, The sharp energy-capacity inequality, Commun. Contemp. Math. 12 (2010) 457 MR2661273
60	M Usher, Boundary depth in Floer theory and its applications to Hamiltonian dynamics and coisotropic submanifolds, Israel J. Math. 184 (2011) 1 MR2823968
61	U Varolgunes, Mayer–Vietoris property for relative symplectic cohomology, Geom. Topol. 25 (2021) 547 MR4251433
62	S Venkatesh, Rabinowitz Floer homology and mirror symmetry, J. Topol. 11 (2018) 144 MR3784228
63	C Viterbo, Functors and computations in Floer homology with applications, I, Geom. Funct. Anal. 9 (1999) 985 MR1726235
64	C Viterbo, Functors and computations in Floer homology with applications, II, preprint (2018) arXiv:1805.01316