Spectral invariants with bulk, quasi-morphisms and Lagrangian floer theory:
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| Main Authors: | , , |
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| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
[2019]
|
| Series: | Memoirs of the American Mathematical Society
volume 260, number 1254 (third of 5 numbers) |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | x, 266 Seiten Illustrationen |
| ISBN: | 9781470436254 |
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MARC
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| 245 | 1 | 0 | |a Spectral invariants with bulk, quasi-morphisms and Lagrangian floer theory |c Kenji Fukaya, Yong-Geun Oh, Hiroshi Ohta, Kaoru Ono |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c [2019] | |
| 264 | 4 | |c © 2019 | |
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| 490 | 1 | |a Memoirs of the American Mathematical Society |v volume 260, number 1254 (third of 5 numbers) | |
| 700 | 1 | |a Oh, Yong-Geun |d 1961- |0 (DE-588)1079551433 |4 aut | |
| 700 | 1 | |a Ono, Kaoru |4 aut | |
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Record in the Search Index
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| adam_text | Contents Preface ix Chapter 1. Introduction 1.1. Introduction 1.2. Notations and Conventions 1.3. Difference between Entov-Polterovich’s convention and ours 1 1 8 13 Part 1. 15 Review of spectral invariants Chapter 2. Hamiltonian Floer-Novikov complex 17 Chapter 3. Floer boundary map 21 Chapter 4. Spectral invariants 31 Part 2. Bulk deformations of Hamiltonian Floer homology and spectral invariants 39 Chapter 5. Big quantum cohomology ring: Review 41 Chapter 6. Hamiltonian Floer homology with bulk deformations 45 Chapter 7. Spectral invariants with bulk deformation 51 Chapter 8. Proof of the spectrality axiom 8.1. Usher’s spectrality lemma 8.2. Proof of nondegenerate spectrality 55 55 58 Chapter 9. 59 Chapter 10. Chapter 11.1. 11.2. 11.3. Proof of C°-Hamiltoman continuity Proof of homotopy invariance 11. Proof of the triangle inequality Pants products Multiplicative property of Piunikhin isomorphism Wrap-up of the proof of triangle inequality Chapter 12. Proofs of other axioms 65 69 69 75 80 81 Part 3. Quasi-states and quasi-morphisms via spectral invariants with bulk 83 Chapter 13. 85 Partial symplectic quasi-states ІІІ
CONTENTS Chapter 14.1. 14.2. 14.3. 14. Construction by spectral invariant with bulk Existence of the limit partial quasi-inorphism property of թէ Partial symplectic quasi-state property of ζ£ 89 90 93 94 Chapter 15.1. 15.2. 15.3. 15.4. 15.5. 15. Poincaré duality and spectral invariant Statement of the result Algebraic preliminary Duality between Floer homologies Duality and Piunikhin isomorphism Proof of Theorem 1.1 97 97 97 98 100 101 Chapter 16. Part 4. Construction of quasi-morphisms via spectral invariant with bulk 103 Spectral invariants and Lagrangian Floer theory Chapter 17. Operator q; review 109 Chapter 18. Criterion for heaviness of Lagrangian submanifolds 18.1. Statement of the results 18.2. Floer homologies of periodic Hamiltonians and of Lagrangian submanifolds 18.3. Filtration and the map 18.4. 18.5. Identity 3^’*η o Heaviness of L Chapter 19. Part 5. Chapter 20.1. 20.2. 20.3. 20.4. 107 = г*ш,ь Linear independence of quasi-morphisms. Applications 20. Lagrangian Floer theory of toric fibers: review Toric manifolds: review Review of Floer cohomology of toric fiber Relationship with the Floer cohomology in Chapter 17 Properties of Floer cohomology HFt({L, b); Л): review 117 117 120 125 126 130 131 133 135 135 136 139 140 Chapter 21. Spectral invariants and quasi-morphisms for toric manifolds 149 21.1. /ig-heaviness of the Lagrangian fibers in toric manifolds 149 21.2. Calculation of the leading order term of the potential function in the toric case: review 150 21.3. Existence of Calabi quasi-morphism on toric manifolds 151 21.4. Defect estimate of a quasi-
morphism թէ 151 Chapter 22. Chapter 23.1. 23.2. 23.3. Lagrangian tori in fc-points blow up of CP2 (к 2) 23. Lagrangian tori in S2 x S2 Review of the construction from [F0006] Superheaviness of T(p) Critical values and eigenvalues of Ci (M) Chapter 24. Lagrangian tori in the cubic surface 153 155 155 156 161 165
CONTKNTS Chapter 25.1. 25.2. 25.3. 25.4. Part 6. 25. Detecting speetral invariant via Ilochschild cohomology Hoehsehild cohomology of filtered Л-*, algebra: review From quantum cohomology to Hochschild cohomology Proof of Theorem 25.1 A remark Appendix Chapter 26. РџЈ j ļt is an isomorphism Chapter 27. Independence on the de Pham representative of b 175 175 170 177 180 181 183 191 Chapter 28.1. 28.2. 28.3. 28.4. 28.5. 28. Proof of Proposition 20.7 Pseudo-isotopy of filtered A,*) algebra Difference between m7 and m Smoothing 2m-invariant chains Wrap-up of the proof of Proposition 3.1 Proof of Lemma 3.3 197 197 199 199 203 207 Chapter 29.1. 29.2. 29.3. 29. Seidel homomorphism with bulk Seidel homomorphism with bulk Proof of Theorem 29.13 Proof of Theorem 29.9 209 209 216 222 Chapter 30. Spectral invariants and Seidel homomorphism 30.1. Valuations and spectral invariants 30.2. The toric case 225 225 227 Part 7. 231 Kuranishi structure and its CF-perturbation: summary Chapter 31. Kuranishi structure arid good coordinate system 31.1. Orbifold 31.2. Kuranishi structure 233 233 234 Chapter 32. Strongly smooth map and fiber product 32.1. Strongly smooth map 32.2. Fiber product 239 239 239 Chapter 33.1. 33.2. 33.3. 241 241 241 244 33. CF perturbation and integration along the fiber Differential form on the space with Kuranishi structure CF-perturbation Integration along the fiber Chapter 34. Stokes’ theorem 34.1. Normalized boundary 34.2. Statement of Stokes’ theorem 249 249 250 Chapter 35.1. 35.2. 35.3. 253 253 254 255 35. Composition formula Smooth correspondence and its
perturbation Composition of smooth correspondences Statement of Composition formula
vi Bibliography Index CONTENTS
|
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| illustrated | Illustrated |
| indexdate | 2024-07-10T08:37:27Z |
| institution | BVB |
| isbn | 9781470436254 |
| language | English |
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| physical | x, 266 Seiten Illustrationen |
| publishDate | 2019 |
| publishDateSearch | 2019 |
| publishDateSort | 2019 |
| publisher | American Mathematical Society |
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| series | Memoirs of the American Mathematical Society |
| series2 | Memoirs of the American Mathematical Society |
| spelling | Fukaya, Kenji 1959- (DE-588)142815144 aut Spectral invariants with bulk, quasi-morphisms and Lagrangian floer theory Kenji Fukaya, Yong-Geun Oh, Hiroshi Ohta, Kaoru Ono Providence, Rhode Island American Mathematical Society [2019] © 2019 x, 266 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society volume 260, number 1254 (third of 5 numbers) Oh, Yong-Geun 1961- (DE-588)1079551433 aut Ono, Kaoru aut Memoirs of the American Mathematical Society volume 260, number 1254 (third of 5 numbers) (DE-604)BV008000141 1254 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031559621&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Fukaya, Kenji 1959- Oh, Yong-Geun 1961- Ono, Kaoru Spectral invariants with bulk, quasi-morphisms and Lagrangian floer theory Memoirs of the American Mathematical Society |
| title | Spectral invariants with bulk, quasi-morphisms and Lagrangian floer theory |
| title_auth | Spectral invariants with bulk, quasi-morphisms and Lagrangian floer theory |
| title_exact_search | Spectral invariants with bulk, quasi-morphisms and Lagrangian floer theory |
| title_full | Spectral invariants with bulk, quasi-morphisms and Lagrangian floer theory Kenji Fukaya, Yong-Geun Oh, Hiroshi Ohta, Kaoru Ono |
| title_fullStr | Spectral invariants with bulk, quasi-morphisms and Lagrangian floer theory Kenji Fukaya, Yong-Geun Oh, Hiroshi Ohta, Kaoru Ono |
| title_full_unstemmed | Spectral invariants with bulk, quasi-morphisms and Lagrangian floer theory Kenji Fukaya, Yong-Geun Oh, Hiroshi Ohta, Kaoru Ono |
| title_short | Spectral invariants with bulk, quasi-morphisms and Lagrangian floer theory |
| title_sort | spectral invariants with bulk quasi morphisms and lagrangian floer theory |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031559621&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
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