Volume 18, issue 4 (2018)

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Symplectic homology and the Eilenberg–Steenrod axioms

Kai Cieliebak and Alexandru Oancea

Appendix: Kai Cieliebak, Alexandru Oancea and Peter Albers

Algebraic & Geometric Topology 18 (2018) 1953–2130
Bibliography
1 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
2 M Abouzaid, P Seidel, Altering symplectic manifolds by homologous recombination, preprint (2010) arXiv:1007.3281
3 M Abouzaid, P Seidel, An open string analogue of Viterbo functoriality, Geom. Topol. 14 (2010) 627 MR2602848
4 P Albers, K Cieliebak, U Frauenfelder, Symplectic Tate homology, Proc. Lond. Math. Soc. 112 (2016) 169 MR3458149
5 P Albers, U Frauenfelder, Leaf-wise intersections and Rabinowitz Floer homology, J. Topol. Anal. 2 (2010) 77 MR2646990
6 P Albers, U Fuchs, W J Merry, Orderability and the Weinstein conjecture, Compos. Math. 151 (2015) 2251 MR3433886
7 D Ayala, J Francis, Factorization homology of topological manifolds, J. Topol. 8 (2015) 1045 MR3431668
8 A A Beĭlinson, J Bernstein, P Deligne, Faisceaux pervers, from: "Analysis and topology on singular spaces, I", Astérisque 100, Soc. Math. France (1982) 5 MR751966
9 P Biran, O Cornea, Lagrangian cobordism, I, J. Amer. Math. Soc. 26 (2013) 295 MR3011416
10 M S Borman, Y Eliashberg, E Murphy, Existence and classification of overtwisted contact structures in all dimensions, Acta Math. 215 (2015) 281 MR3455235
11 C. Bounya, Lagrangian Rabinowitz–Floer homology, unpublished manuscript
12 F Bourgeois, T Ekholm, Y Eliashberg, Symplectic homology product via Legendrian surgery, Proc. Natl. Acad. Sci. USA 108 (2011) 8114 MR2806647
13 F Bourgeois, T Ekholm, Y Eliashberg, Effect of Legendrian surgery, Geom. Topol. 16 (2012) 301 MR2916289
14 F Bourgeois, Y Eliashberg, H Hofer, K Wysocki, E Zehnder, Compactness results in symplectic field theory, Geom. Topol. 7 (2003) 799 MR2026549
15 F Bourgeois, A Oancea, An exact sequence for contact- and symplectic homology, Invent. Math. 175 (2009) 611 MR2471597
16 F Bourgeois, A Oancea, Symplectic homology, autonomous Hamiltonians, and Morse–Bott moduli spaces, Duke Math. J. 146 (2009) 71 MR2475400
17 F Bourgeois, A Oancea, The Gysin exact sequence for S1–equivariant symplectic homology, J. Topol. Anal. 5 (2013) 361 MR3152208
18 F Bourgeois, A Oancea, S1–equivariant symplectic homology and linearized contact homology, Int. Math. Res. Not. 2017 (2017) 3849 MR3671507
19 F Bourgeois, O v Koert, Linearized contact homology of connected sums, unpublished manuscript
20 G E Bredon, Topology and geometry, 139, Springer (1993) MR1224675
21 R Casals, E Murphy, F Presas, Geometric criteria for overtwistedness, preprint (2015) arXiv:1503.06221
22 B Chantraine, G Dimitroglou Rizell, P Ghiggini, R Golovko, Floer homology and Lagrangian concordance, from: "Proceedings of the Gökova Geometry–Topology Conference 2014" (editors S Akbulut, D Auroux, T Önder), GGT (2015) 76 MR3381440
23 H Chen, D Lee, A remark on equivariant Poincaré duality, J. Pure Appl. Algebra 74 (1991) 239 MR1135029
24 K Cieliebak, Handle attaching in symplectic homology and the chord conjecture, J. Eur. Math. Soc. 4 (2002) 115 MR1911873
25 K Cieliebak, Y Eliashberg, From Stein to Weinstein and back : symplectic geometry of affine complex manifolds, 59, Amer. Math. Soc. (2012) MR3012475
26 K Cieliebak, A Floer, H Hofer, Symplectic homology, II : A general construction, Math. Z. 218 (1995) 103 MR1312580
27 K Cieliebak, U A Frauenfelder, A Floer homology for exact contact embeddings, Pacific J. Math. 239 (2009) 251 MR2461235
28 K Cieliebak, U Frauenfelder, Morse homology on noncompact manifolds, J. Korean Math. Soc. 48 (2011) 749 MR2840523
29 K Cieliebak, U Frauenfelder, A Oancea, Rabinowitz Floer homology and symplectic homology, Ann. Sci. Éc. Norm. Supér. 43 (2010) 957 MR2778453
30 K Cieliebak, K Mohnke, Compactness for punctured holomorphic curves, J. Symplectic Geom. 3 (2005) 589 MR2235856
31 G Dimitroglou Rizell, Lifting pseudo-holomorphic polygons to the symplectisation of P × and applications, Quantum Topol. 7 (2016) 29 MR3459958
32 G Dimitroglou Rizell, R Golovko, On homological rigidity and flexibility of exact Lagrangian endocobordisms, Internat. J. Math. 25 (2014) MR3275826
33 S Eilenberg, S Mac Lane, On the groups H,n), I, Ann. of Math. 58 (1953) 55 MR0056295
34 S Eilenberg, N Steenrod, Foundations of algebraic topology, Princeton Univ. Press (1952) MR0050886
35 T Ekholm, Rational SFT, linearized Legendrian contact homology, and Lagrangian Floer cohomology, from: "Perspectives in analysis, geometry, and topology" (editors I Itenberg, B Jöricke, M Passare), Progr. Math. 296, Springer (2012) 109 MR2884034
36 T Ekholm, J B Etnyre, J M Sabloff, A duality exact sequence for Legendrian contact homology, Duke Math. J. 150 (2009) 1 MR2560107
37 T Ekholm, J Etnyre, M Sullivan, The contact homology of Legendrian submanifolds in 2n+1, J. Differential Geom. 71 (2005) 177 MR2197142
38 T Ekholm, K Honda, T Kálmán, Legendrian knots and exact Lagrangian cobordisms, J. Eur. Math. Soc. 18 (2016) 2627 MR3562353
39 T Ekholm, A Oancea, Symplectic and contact differential graded algebras, Geom. Topol. 21 (2017) 2161 MR3654106
40 Y Eliashberg, A Givental, H Hofer, Introduction to symplectic field theory, Geom. Funct. Anal. (2000) 560 MR1826267
41 J R Espina, The mean Euler characteristic of contact structures, PhD thesis, University of California, Santa Cruz (2011) MR2926815
42 A Floer, H Hofer, Symplectic homology, I : Open sets in n, Math. Z. 215 (1994) 37 MR1254813
43 K Fukaya, P Seidel, I Smith, The symplectic geometry of cotangent bundles from a categorical viewpoint, from: "Homological mirror symmetry" (editors A Kapustin, M Kreuzer, K G Schlesinger), Lecture Notes in Phys. 757, Springer (2009) 1 MR2596633
44 R Golovko, A note on Lagrangian cobordisms between Legendrian submanifolds of 2n+1, Pacific J. Math. 261 (2013) 101 MR3037561
45 T G Goodwillie, Cyclic homology, derivations, and the free loopspace, Topology 24 (1985) 187 MR793184
46 M Goresky, N Hingston, Loop products and closed geodesics, Duke Math. J. 150 (2009) 117 MR2560110
47 J Gutt, The positive equivariant symplectic homology as an invariant for some contact manifolds, J. Symplectic Geom. 15 (2017) 1019 MR3734608
48 J Gutt, J Kang, On the minimal number of periodic orbits on some hypersurfaces in 2n, Ann. Inst. Fourier (Grenoble) 66 (2016) 2485 MR3580178
49 K Hess, Multiplicative structure in equivariant cohomology, J. Pure Appl. Algebra 216 (2012) 1680 MR2899830
50 C E Hood, J D S Jones, Some algebraic properties of cyclic homology groups, K–Theory 1 (1987) 361 MR920950
51 J D S Jones, Cyclic homology and equivariant homology, Invent. Math. 87 (1987) 403 MR870737
52 J D S Jones, S B Petrack, The fixed point theorem in equivariant cohomology, Trans. Amer. Math. Soc. 322 (1990) 35 MR1010411
53 J Kang, Symplectic homology of displaceable Liouville domains and leafwise intersection points, Geom. Dedicata 170 (2014) 135 MR3199480
54 M Kashiwara, P Schapira, Sheaves on manifolds, 292, Springer (1990) MR1074006
55 M Kwon, O van Koert, Brieskorn manifolds in contact topology, Bull. Lond. Math. Soc. 48 (2016) 173 MR3483060
56 P Massot, K Niederkrüger, C Wendl, Weak and strong fillability of higher dimensional contact manifolds, Invent. Math. 192 (2013) 287 MR3044125
57 J P May, The additivity of traces in triangulated categories, Adv. Math. 163 (2001) 34 MR1867203
58 M Maydanskiy, Exotic symplectic manifolds from Lefschetz fibrations, preprint (2009) arXiv:0906.2224
59 W J Merry, Lagrangian Rabinowitz Floer homology and twisted cotangent bundles, Geom. Dedicata 171 (2014) 345 MR3226800
60 E Moro, Dual space question, MathStackExchange (2012)
61 E Murphy, K Siegel, Subflexible symplectic manifolds, preprint (2015) arXiv:1510.01867
62 L Polterovich, E Shelukhin, Autonomous Hamiltonian flows, Hofer’s geometry and persistence modules, Selecta Math. 22 (2016) 227 MR3437837
63 A F Ritter, Novikov-symplectic cohomology and exact Lagrangian embeddings, Geom. Topol. 13 (2009) 943 MR2470967
64 A F Ritter, Topological quantum field theory structure on symplectic cohomology, J. Topol. 6 (2013) 391 MR3065181
65 D Salamon, E Zehnder, Morse theory for periodic solutions of Hamiltonian systems and the Maslov index, Comm. Pure Appl. Math. 45 (1992) 1303 MR1181727
66 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
67 P Uebele, Periodic Reeb flows and products in symplectic homology, preprint (2015) arXiv:1512.06208
68 C Viterbo, Functors and computations in Floer homology with applications, I, Geom. Funct. Anal. 9 (1999) 985 MR1726235
69 C A Weibel, An introduction to homological algebra, 38, Cambridge Univ. Press (1994) MR1269324
70 M L Yau, Cylindrical contact homology of subcritical Stein-fillable contact manifolds, Geom. Topol. 8 (2004) 1243 MR2087083
71 J Zhao, Periodic symplectic cohomologies, preprint (2014) arXiv:1405.2084