Algebraic & Geometric Topology Volume 19, issue 7 (2019)

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Symplectic structure perturbations and continuity of symplectic invariants

Jun Zhang

Algebraic & Geometric Topology 19 (2019) 3261–3314

DOI: 10.2140/agt.2019.19.3261

Bibliography

1	G Carlsson, A Zomorodian, The theory of multidimensional persistence, Discrete Comput. Geom. 42 (2009) 71 MR2506738
2	J M Cohen, Zero divisors in group rings, Comm. Algebra 2 (1974) 1 MR344280
3	M Entov, Quasi-morphisms and quasi-states in symplectic topology, from: "Proceedings of the International Congress of Mathematicians" (editors S Y Jang, Y R Kim, D W Lee, I Ye), Kyung Moon Sa (2014) 1147 MR3728656
4	M Entov, L Polterovich, Calabi quasimorphism and quantum homology, Int. Math. Res. Not. 2003 (2003) 1635 MR1979584
5	M Entov, L Polterovich, Symplectic quasi-states and semi-simplicity of quantum homology, from: "Toric topology" (editors M Harada, Y Karshon, M Masuda, T Panov), Contemp. Math. 460, Amer. Math. Soc. (2008) 47 MR2428348
6	M Entov, L Polterovich, Rigid subsets of symplectic manifolds, Compos. Math. 145 (2009) 773 MR2507748
7	A Floer, Symplectic fixed points and holomorphic spheres, Comm. Math. Phys. 120 (1989) 575 MR987770
8	U Frauenfelder, V Ginzburg, F Schlenk, Energy capacity inequalities via an action selector, from: "Geometry, spectral theory, groups, and dynamics" (editors M Entov, Y Pinchover, M Sageev), Contemp. Math. 387, Amer. Math. Soc. (2005) 129 MR2179791
9	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
10	V Humilière, F Le Roux, S Seyfaddini, Towards a dynamical interpretation of Hamiltonian spectral invariants on surfaces, Geom. Topol. 20 (2016) 2253 MR3548467
11	S Ishikawa, Spectral invariants of distance functions, J. Topol. Anal. 8 (2016) 655 MR3545016
12	M Kawasaki, Superheavy Lagrangian immersions in surfaces, J. Symplectic Geom. 17 (2019) 239 MR3956374
13	H Lê, The Calabi invariant and the least number of periodic solutions of locally Hamiltonian equations, preprint (2015) arXiv:1511.00638
14	Y G Oh, Construction of spectral invariants of Hamiltonian paths on closed symplectic manifolds, from: "The breadth of symplectic and Poisson geometry" (editors J E Marsden, T S Ratiu), Progr. Math. 232, Birkhäuser (2005) 525 MR2103018
15	Y G Oh, Floer mini-max theory, the Cerf diagram, and the spectral invariants, J. Korean Math. Soc. 46 (2009) 363 MR2494501
16	K Ono, Floer–Novikov cohomology and symplectic fixed points, J. Symplectic Geom. 3 (2005) 545 MR2235854
17	Y Ostrover, A comparison of Hofer’s metrics on Hamiltonian diffeomorphisms and Lagrangian submanifolds, Commun. Contemp. Math. 5 (2003) 803 MR2017719
18	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
19	J Robbin, D Salamon, The Maslov index for paths, Topology 32 (1993) 827 MR1241874
20	J J Rotman, An introduction to homological algebra, Springer (2009) MR2455920
21	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
22	M Schwarz, On the action spectrum for closed symplectically aspherical manifolds, Pacific J. Math. 193 (2000) 419 MR1755825
23	M Usher, Spectral numbers in Floer theories, Compos. Math. 144 (2008) 1581 MR2474322
24	M Usher, The sharp energy-capacity inequality, Commun. Contemp. Math. 12 (2010) 457 MR2661273
25	M Usher, Boundary depth in Floer theory and its applications to Hamiltonian dynamics and coisotropic submanifolds, Israel J. Math. 184 (2011) 1 MR2823968
26	M Usher, Many closed symplectic manifolds have infinite Hofer–Zehnder capacity, Trans. Amer. Math. Soc. 364 (2012) 5913 MR2946937
27	M Usher, Hofer’s metrics and boundary depth, Ann. Sci. Éc. Norm. Supér. 46 (2013) 57 MR3087390
28	M Usher, J Zhang, Persistent homology and Floer–Novikov theory, Geom. Topol. 20 (2016) 3333 MR3590354
29	L H Vân, K Ono, Symplectic fixed points, the Calabi invariant and Novikov homology, Topology 34 (1995) 155 MR1308493
30	C Viterbo, Symplectic topology as the geometry of generating functions, Math. Ann. 292 (1992) 685 MR1157321