Geometry & Topology Volume 20, issue 6 (2016)

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1364-0380 (online)

ISSN 1465-3060 (print)

Author Index

To Appear

Other MSP Journals

Persistent homology and Floer–Novikov theory

Michael Usher and Jun Zhang

Geometry & Topology 20 (2016) 3333–3430

DOI: 10.2140/gt.2016.20.3333

Bibliography

1	M Audin, M Damian, Morse theory and Floer homology, Springer (2014) MR3155456
2	S A Barannikov, The framed Morse complex and its invariants, from: "Singularities and bifurcations" (editor V I Arnol’d), Adv. Soviet Math. 21, Amer. Math. Soc. (1994) 93 MR1310596
3	U Bauer, M Lesnick, Induced matchings and the algebraic stability of persistence barcodes, J. Comput. Geom. 6 (2015) 162 MR3333456
4	P Biran, O Cornea, Rigidity and uniruling for Lagrangian submanifolds, Geom. Topol. 13 (2009) 2881 MR2546618
5	D Burghelea, T K Dey, Topological persistence for circle-valued maps, Discrete Comput. Geom. 50 (2013) 69 MR3070542
6	D Burghelea, S Haller, Topology of angle valued maps, bar codes and Jordan blocks, preprint (2013) arXiv:1303.4328
7	G Carlsson, Topology and data, Bull. Amer. Math. Soc. 46 (2009) 255 MR2476414
8	F Chazal, D Cohen-Steiner, M Glisse, L Guibas, S Oudot, Proximity of persistence modules and their diagrams, from: "Computational geometry", ACM (2009) 237
9	F Chazal, V de Silva, M Glisse, S Oudot, The structure and stability of persistence modules, preprint (2012) arXiv:1207.3674
10	D Cohen-Steiner, H Edelsbrunner, J Harer, Stability of persistence diagrams, Discrete Comput. Geom. 37 (2007) 103 MR2279866
11	O Cornea, A Ranicki, Rigidity and gluing for Morse and Novikov complexes, J. Eur. Math. Soc. 5 (2003) 343 MR2017851
12	W Crawley-Boevey, Decomposition of pointwise finite-dimensional persistence modules, J. Algebra Appl. 14 (2015) MR3323327
13	M Entov, L Polterovich, Calabi quasimorphism and quantum homology, Int. Math. Res. Not. 2003 (2003) 1635 MR1979584
14	M Farber, Topology of closed one-forms, 108, Amer. Math. Soc. (2004) MR2034601
15	A Floer, An instanton-invariant for 3–manifolds, Comm. Math. Phys. 118 (1988) 215 MR956166
16	A Floer, Morse theory for Lagrangian intersections, J. Differential Geom. 28 (1988) 513 MR965228
17	A Floer, Symplectic fixed points and holomorphic spheres, Comm. Math. Phys. 120 (1989) 575 MR987770
18	A Floer, H Hofer, Symplectic homology, I : Open sets in ℂⁿ, Math. Z. 215 (1994) 37 MR1254813
19	U Frauenfelder, The Arnold–Givental conjecture and moment Floer homology, Int. Math. Res. Not. 2004 (2004) 2179 MR2076142
20	K Fukaya, Y G Oh, H Ohta, K Ono, Lagrangian intersection Floer theory : anomaly and obstruction, Volume I, 46, Amer. Math. Soc. (2009) MR2553465
21	K Fukaya, Y G Oh, H Ohta, K Ono, Displacement of polydisks and Lagrangian Floer theory, J. Symplectic Geom. 11 (2013) 231 MR3046491
22	K Fukaya, K Ono, Arnold conjecture and Gromov–Witten invariant, Topology 38 (1999) 933 MR1688434
23	R Ghrist, Barcodes: the persistent topology of data, Bull. Amer. Math. Soc. 45 (2008) 61 MR2358377
24	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
25	H Hofer, E Zehnder, Symplectic invariants and Hamiltonian dynamics, Birkhäuser (1994) MR1306732
26	V Humilière, R Leclercq, S Seyfaddini, Coisotropic rigidity and C⁰–symplectic geometry, Duke Math. J. 164 (2015) 767 MR3322310
27	K S Kedlaya, p–adic differential equations, 125, Cambridge Univ. Press (2010) MR2663480
28	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
29	Y J Lee, Reidemeister torsion in Floer–Novikov theory and counting pseudo-holomorphic tori, I, J. Symplectic Geom. 3 (2005) 221 MR2199540
30	G Liu, G Tian, Floer homology and Arnold conjecture, J. Differential Geom. 49 (1998) 1 MR1642105
31	A F Monna, T A Springer, Sur la structure des espaces de Banach non-archimédiens, Nederl. Akad. Wetensch. Proc. Ser. A 27 (1965) 602 MR0187061
32	M Morse, The calculus of variations in the large, 18, Amer. Math. Soc. (1934) MR1451874
33	S P Novikov, Multivalued functions and functionals : an analogue of the Morse theory, Dokl. Akad. Nauk SSSR 260 (1981) 31 MR630459
34	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
35	J Pardon, An algebraic approach to virtual fundamental cycles on moduli spaces of pseudo-holomorphic curves, Geom. Topol. 20 (2016) 779 MR3493097
36	L Polterovich, E Shelukhin, Autonomous Hamiltonian flows, Hofer’s geometry and persistence modules, Selecta Math. 22 (2016) 227 MR3437837
37	J Robbin, D Salamon, The Maslov index for paths, Topology 32 (1993) 827 MR1241874
38	D Salamon, Lectures on Floer homology, lecture notes (1997)
39	M Schwarz, Morse homology, 111, Birkhäuser (1993) MR1239174
40	M Schwarz, On the action spectrum for closed symplectically aspherical manifolds, Pacific J. Math. 193 (2000) 419 MR1755825
41	V de Silva, D Morozov, M Vejdemo-Johansson, Dualities in persistent (co)homology, Inverse Problems 27 (2011) 1 MR2854319
42	M Usher, Spectral numbers in Floer theories, Compos. Math. 144 (2008) 1581 MR2474322
43	M Usher, Duality in filtered Floer–Novikov complexes, J. Topol. Anal. 2 (2010) 233 MR2652908
44	M Usher, Boundary depth in Floer theory and its applications to Hamiltonian dynamics and coisotropic submanifolds, Israel J. Math. 184 (2011) 1 MR2823968
45	M Usher, Hofer’s metrics and boundary depth, Ann. Sci. Éc. Norm. Supér. 46 (2013) 57 MR3087390
46	A Zomorodian, G Carlsson, Computing persistent homology, Discrete Comput. Geom. 33 (2005) 249 MR2121296