Download this article
Download this article For screen
For printing
Recent Issues

Volume 25, 1 issue

Volume 24, 9 issues

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1472-2739 (online)
ISSN 1472-2747 (print)
Author Index
To Appear
 
Other MSP Journals
A Leray–Serre spectral sequence for Lagrangian Floer theory

Douglas Schultz

Algebraic & Geometric Topology 22 (2022) 3171–3248
Bibliography
1 M Akveld, D Salamon, Loops of Lagrangian submanifolds and pseudoholomorphic discs, Geom. Funct. Anal. 11 (2001) 609 MR1866797
2 L Amorim, The Künneth theorem for the Fukaya algebra of a product of Lagrangians, Internat. J. Math. 28 (2017) MR3639044
3 B H An, Y Cho, J S Kim, On the f–vectors of Gelfand–Cetlin polytopes, European J. Combin. 67 (2018) 61 MR3707218
4 M Audin, Torus actions on symplectic manifolds, 93, Birkhäuser (2004) MR2091310
5 M Audin, M Damian, Morse theory and Floer homology, Springer (2014) MR3155456
6 D Auroux, D Gayet, J P Mohsen, Symplectic hypersurfaces in the complement of an isotropic submanifold, Math. Ann. 321 (2001) 739 MR1872527
7 P Biran, O Cornea, Quantum structures for Lagrangian submanifolds, preprint (2007) arXiv:0708.4221
8 P Biran, M Khanevsky, A Floer–Gysin exact sequence for Lagrangian submanifolds, Comment. Math. Helv. 88 (2013) 899 MR3134415
9 F Bourgeois, A Oancea, The Gysin exact sequence for S1–equivariant symplectic homology, J. Topol. Anal. 5 (2013) 361 MR3152208
10 F Charest, C Woodward, Floer trajectories and stabilizing divisors, J. Fixed Point Theory Appl. 19 (2017) 1165 MR3659006
11 F Charest, C T Woodward, Floer cohomology and flips, 1372, Amer. Math. Soc. (2022) MR4464438
12 Y Cho, Y Kim, Y G Oh, Lagrangian fibers of Gelfand–Cetlin systems, Adv. Math. 372 (2020) 107304, 57 MR4126721
13 Y Cho, Y Kim, Y G Oh, A critical point analysis of Landau–Ginzburg potentials with bulk in Gelfand–Cetlin systems, Kyoto J. Math. 61 (2021) 259 MR4342377
14 K Cieliebak, K Mohnke, Symplectic hypersurfaces and transversality in Gromov–Witten theory, J. Symplectic Geom. 5 (2007) 281 MR2399678
15 S K Donaldson, Symplectic submanifolds and almost-complex geometry, J. Differential Geom. 44 (1996) 666 MR1438190
16 K Fukaya, Y G Oh, H Ohta, K Ono, Lagrangian intersection Floer theory II : Anomaly and obstruction, 46, Amer. Math. Soc. (2009) MR2548482
17 E González, C T Woodward, Quantum cohomology and toric minimal model programs, Adv. Math. 353 (2019) 591 MR3986375
18 M Gromov, Pseudo holomorphic curves in symplectic manifolds, Invent. Math. 82 (1985) 307 MR809718
19 V Guillemin, E Lerman, S Sternberg, Symplectic fibrations and multiplicity diagrams, Cambridge Univ. Press (1996) MR1414677
20 V Guillemin, S Sternberg, The Gel’fand–Cetlin system and quantization of the complex flag manifolds, J. Funct. Anal. 52 (1983) 106 MR705993
21 M Hutchings, Floer homology of families, I, Algebr. Geom. Topol. 8 (2008) 435 MR2443235
22 L Lazzarini, Relative frames on J–holomorphic curves, J. Fixed Point Theory Appl. 9 (2011) 213 MR2821362
23 J Leray, L’anneau spectral et l’anneau filtré d’homologie d’un espace localement compact et d’une application continue, J. Math. Pures Appl. 29 (1950) 1 MR37505
24 J Leray, L’homologie d’un espace fibré dont la fibre est connexe, J. Math. Pures Appl. 29 (1950) 169 MR39256
25 D McDuff, D Salamon, J–holomorphic curves and symplectic topology, 52, Amer. Math. Soc. (2004) MR2045629
26 D McDuff, D Salamon, Introduction to symplectic topology, Oxford Univ. Press (2017) MR3674984
27 T Nishinou, Y Nohara, K Ueda, Toric degenerations of Gelfand–Cetlin systems and potential functions, Adv. Math. 224 (2010) 648 MR2609019
28 Y Nohara, K Ueda, Floer cohomologies of non-torus fibers of the Gelfand–Cetlin system, J. Symplectic Geom. 14 (2016) 1251 MR3601889
29 A Oancea, The Künneth formula in Floer homology for manifolds with restricted contact type boundary, Math. Ann. 334 (2006) 65 MR2208949
30 A Oancea, Fibered symplectic cohomology and the Leray–Serre spectral sequence, J. Symplectic Geom. 6 (2008) 267 MR2448827
31 Y G Oh, Floer cohomology, spectral sequences, and the Maslov class of Lagrangian embeddings, Internat. Math. Res. Notices (1996) 305 MR1389956
32 M Pabiniak, Displacing (Lagrangian) submanifolds in the manifolds of full flags, Adv. Geom. 15 (2015) 101 MR3300713
33 T Perutz, A symplectic Gysin sequence, preprint (2008) arXiv:0807.1863
34 D Schultz, Holomorphic disks and the disk potential for a fibered Lagrangian, J. Symplectic Geom. 19 (2021) 143 MR4325385
35 P Seidel, Graded Lagrangian submanifolds, Bull. Soc. Math. France 128 (2000) 103 MR1765826
36 T Sodoge, The geometry and topology of stable coisotropic submanifolds, PhD thesis, University College London (2017)
37 C A Weibel, An introduction to homological algebra, 38, Cambridge Univ. Press (1994) MR1269324