Geometry & Topology Volume 25, issue 6 (2021)

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Barcodes and area-preserving homeomorphisms

Frédéric Le Roux, Sobhan Seyfaddini and Claude Viterbo

Geometry & Topology 25 (2021) 2713–2825

DOI: 10.2140/gt.2021.25.2713

Bibliography

1	S A Barannikov, The framed Morse complex and its invariants, from: "Singularities and bifurcations" (editor V I Arnold), Adv. Soviet Math. 21, Amer. Math. Soc. (1994) 93 MR1310596
2	F Béguin, S Crovisier, F Le Roux, Pseudo-rotations of the open annulus, Bull. Braz. Math. Soc. 37 (2006) 275 MR2266384
3	M Bonino, A dynamical property for planar homeomorphisms and an application to the problem of canonical position around an isolated fixed point, Topology 40 (2001) 1241 MR1867244
4	L Buhovsky, V Humilière, S Seyfaddini, The action spectrum and C⁰ symplectic topology, Math. Ann. 380 (2021) 293 MR4263685
5	F Chazal, D Cohen-Steiner, M Glisse, L J Guibas, S Y Oudot, Proximity of persistence modules and their diagrams, from: "Proceedings of the Twenty-fifth Annual Symposium on Computational Geometry", ACM (2009) 237
6	F Chazal, V de Silva, M Glisse, S Oudot, The structure and stability of persistence modules, Springer (2016) MR3524869
7	K Cieliebak, A Floer, H Hofer, K Wysocki, Applications of symplectic homology, II : Stability of the action spectrum, Math. Z. 223 (1996) 27 MR1408861
8	D Cohen-Steiner, H Edelsbrunner, J Harer, Stability of persistence diagrams, Discrete Comput. Geom. 37 (2007) 103 MR2279866
9	J Conejeros, The local rotation set is an interval, Ergodic Theory Dynam. Systems 38 (2018) 2571 MR3846718
10	C Conley, Isolated invariant sets and the Morse index, 38, Amer. Math. Soc. (1978) MR511133
11	M Entov, L Polterovich, P Py, On continuity of quasimorphisms for symplectic maps, from: "Perspectives in analysis, geometry, and topology" (editors I Itenberg, B Jöricke, M Passare), Progr. Math. 296, Springer (2012) 169 MR2884036
12	A Fathi, Structure of the group of homeomorphisms preserving a good measure on a compact manifold, Ann. Sci. École Norm. Sup. 13 (1980) 45 MR584082
13	A Floer, Cuplength estimates on Lagrangian intersections, Comm. Pure Appl. Math. 42 (1989) 335 MR990135
14	A Floer, Symplectic fixed points and holomorphic spheres, Comm. Math. Phys. 120 (1989) 575 MR987770
15	A Floer, Witten’s complex and infinite-dimensional Morse theory, J. Differential Geom. 30 (1989) 207 MR1001276
16	J M Gambaudo, É Ghys, Commutators and diffeomorphisms of surfaces, Ergodic Theory Dynam. Systems 24 (2004) 1591 MR2104597
17	V L Ginzburg, The Conley conjecture, Ann. of Math. 172 (2010) 1127 MR2680488
18	V L Ginzburg, B Z Gürel, Action and index spectra and periodic orbits in Hamiltonian dynamics, Geom. Topol. 13 (2009) 2745 MR2529945
19	V L Ginzburg, B Z Gürel, Local Floer homology and the action gap, J. Symplectic Geom. 8 (2010) 323 MR2684510
20	E Glasner, B Weiss, The topological Rohlin property and topological entropy, Amer. J. Math. 123 (2001) 1055 MR1867311
21	E Glasner, B Weiss, Topological groups with Rokhlin properties, Colloq. Math. 110 (2008) 51 MR2353899
22	L Guillou, On the structure of homeomorphisms of the open annulus, Ann. Fac. Sci. Toulouse Math. 20 (2011) 367 MR2847887
23	A Hatcher, Algebraic topology, Cambridge Univ. Press (2002) MR1867354
24	A Hatcher, The Kirby torus trick for surfaces, preprint (2013) arXiv:1312.3518
25	N Hingston, Subharmonic solutions of Hamiltonian equations on tori, Ann. of Math. 170 (2009) 529 MR2552101
26	H Hofer, Lusternik–Schnirelman-theory for Lagrangian intersections, Ann. Inst. H. Poincaré Anal. Non Linéaire 5 (1988) 465 MR970850
27	L Hörmander, Fourier integral operators, I, Acta Math. 127 (1971) 79 MR388463
28	M Kashiwara, P Schapira, Sheaves on manifolds, 292, Springer (1990) MR1074006
29	M Kashiwara, P Schapira, Persistent homology and microlocal sheaf theory, J. Appl. Comput. Topol. 2 (2018) 83 MR3873181
30	A Katok, B Hasselblatt, Introduction to the modern theory of dynamical systems, 54, Cambridge Univ. Press (1995) MR1326374
31	A Kislev, E Shelukhin, Bounds on spectral norms and barcodes, preprint (2018) arXiv:1810.09865
32	F Lalonde, D McDuff, The geometry of symplectic energy, Ann. of Math. 141 (1995) 349 MR1324138
33	F Laudenbach, On an article by S A Barannikov, preprint (2015) arXiv:1509.03490
34	F Laudenbach, J C Sikorav, Persistance d’intersection avec la section nulle au cours d’une isotopie hamiltonienne dans un fibré cotangent, Invent. Math. 82 (1985) 349 MR809719
35	P Le Calvez, Une propriété dynamique des homéomorphismes du plan au voisinage d’un point fixe d’indice > 1, Topology 38 (1999) 23 MR1644067
36	P Le Calvez, Dynamique des homéomorphismes du plan au voisinage d’un point fixe, Ann. Sci. École Norm. Sup. 36 (2003) 139 MR1987979
37	P Le Calvez, Une version feuilletée équivariante du théorème de translation de Brouwer, Publ. Math. Inst. Hautes Études Sci. 102 (2005) 1 MR2217051
38	P Le Calvez, Pourquoi les points périodiques des homéomorphismes du plan tournent-ils autour de certains points fixes ?, Ann. Sci. Éc. Norm. Supér. 41 (2008) 141 MR2423312
39	P Le Calvez, J C Yoccoz, Un théorème d’indice pour les homéomorphismes du plan au voisinage d’un point fixe, Ann. of Math. 146 (1997) 241 MR1477759
40	D Le Peutrec, F Nier, C Viterbo, Precise Arrhenius law for p–forms : the Witten Laplacian and Morse–Barannikov complex, Ann. Henri Poincaré 14 (2013) 567 MR3035640
41	F Le Roux, Homéomorphismes de surfaces : théorèmes de la fleur de Leau–Fatou et de la variété stable, 292, Soc. Math. France (2004) MR2068866
42	F Le Roux, Simplicity of Homeo(𝔻²,∂𝔻²,Area) and fragmentation of symplectic diffeomorphisms, J. Symplectic Geom. 8 (2010) 73 MR2609630
43	F Le Roux, L’ensemble de rotation autour d’un point fixe, 350, Soc. Math. France (2013) MR3112082
44	K Mann, M Wolff, Rigidity of mapping class group actions on S¹, Geom. Topol. 24 (2020) 1211 MR4157553
45	C K McCord, On the Hopf index and the Conley index, Trans. Amer. Math. Soc. 313 (1989) 853 MR961594
46	N A Nikišin, Fixed points of the diffeomorphisms of the two-sphere that preserve oriented area, Funkcional. Anal. i Priložen. 8 (1974) 90 MR0346846
47	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
48	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
49	Y G Oh, S Müller, The group of Hamiltonian homeomorphisms and C⁰–symplectic topology, J. Symplectic Geom. 5 (2007) 167 MR2377251
50	Y Ostrover, A comparison of Hofer’s metrics on Hamiltonian diffeomorphisms and Lagrangian submanifolds, Commun. Contemp. Math. 5 (2003) 803 MR2017719
51	J C Oxtoby, S M Ulam, Measure-preserving homeomorphisms and metrical transitivity, Ann. of Math. 42 (1941) 874 MR5803
52	A Patou, Arcs libres d’homéomorphismes en dimension 2, PhD thesis, Université Joseph Fourier, Grenoble (2006)
53	S Pelikan, E E Slaminka, A bound for the fixed point index of area-preserving homeomorphisms of two-manifolds, Ergodic Theory Dynam. Systems 7 (1987) 463 MR912377
54	L Polterovich, The geometry of the group of symplectic diffeomorphisms, Birkhäuser (2001) MR1826128
55	L Polterovich, D Rosen, K Samvelyan, J Zhang, Topological persistence in geometry and analysis, 74, Amer. Math. Soc. (2020) MR4249570
56	L Polterovich, E Shelukhin, Autonomous Hamiltonian flows, Hofer’s geometry and persistence modules, Selecta Math. 22 (2016) 227 MR3437837
57	L Polterovich, E Shelukhin, V Stojisavljević, Persistence modules with operators in Morse and Floer theory, Mosc. Math. J. 17 (2017) 757 MR3734662
58	P E Pushkar, Y V Chekanov, Combinatorics of fronts of Legendrian links, and Arnold’s 4–conjectures, Uspekhi Mat. Nauk 60 (2005) 99 MR2145660
59	B V Schmitt, L’espace des homéomorphismes du plan qui admettent un seul point fixe d’indice donné est connexe par arcs, Topology 18 (1979) 235 MR546793
60	S Seyfaddini, C⁰–limits of Hamiltonian paths and the Oh–Schwarz spectral invariants, Int. Math. Res. Not. 2013 (2013) 4920 MR3123670
61	S Seyfaddini, Spectral killers and Poisson bracket invariants, J. Mod. Dyn. 9 (2015) 51 MR3395260
62	E Shelukhin, Viterbo conjecture for Zoll symmetric spaces, preprint (2018) arXiv:1811.05552
63	J C Sikorav, Points fixes d’une application symplectique homologue à l’identité, J. Differential Geom. 22 (1985) 49 MR826424
64	C P Simon, A bound for the fixed-point index of an area-preserving map with applications to mechanics, Invent. Math. 26 (1974) 187 MR353372
65	E E Slaminka, Removing index 0 fixed points for area preserving maps of two-manifolds, Trans. Amer. Math. Soc. 340 (1993) 429 MR1145963
66	M Usher, The sharp energy-capacity inequality, Commun. Contemp. Math. 12 (2010) 457 MR2661273
67	M Usher, J Zhang, Persistent homology and Floer–Novikov theory, Geom. Topol. 20 (2016) 3333 MR3590354
68	C Viterbo, Symplectic topology as the geometry of generating functions, Math. Ann. 292 (1992) 685 MR1157321
69	C Viterbo, Functors and computations in Floer homology with applications, II, preprint (2018) arXiv:1805.01316
70	A Zomorodian, G Carlsson, Computing persistent homology, Discrete Comput. Geom. 33 (2005) 249 MR2121296