| Description |
1 online resource (x, 266 pages) |
| Series |
Memoirs of the American Mathematical Society, 1947-6221 ; volume 260, number 1254 |
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Memoirs of the American Mathematical Society ; no. 1254.
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| Contents |
Cover; Title page; Preface; Chapter 1. Introduction; 1.1. Introduction; 1.2. Notations and Conventions; 1.3. Difference between Entov-Polterovich's convention and ours; Part 1 . Review of spectral invariants; Chapter 2. Hamiltonian Floer-Novikov complex; Chapter 3. Floer boundary map; Chapter 4. Spectral invariants; Part 2 . Bulk deformations of Hamiltonian Floer homology and spectral invariants; Chapter 5. Big quantum cohomology ring: Review; Chapter 6. Hamiltonian Floer homology with bulk deformations; Chapter 7. Spectral invariants with bulk deformation |
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Chapter 8. Proof of the spectrality axiom8.1. Usher's spectrality lemma; 8.2. Proof of nondegenerate spectrality; Chapter 9. Proof of ⁰-Hamiltonian continuity; Chapter 10. Proof of homotopy invariance; Chapter 11. Proof of the triangle inequality; 11.1. Pants products; 11.2. Multiplicative property of Piunikhin isomorphism; 11.3. Wrap-up of the proof of triangle inequality; Chapter 12. Proofs of other axioms; Part 3 . Quasi-states and quasi-morphisms via spectral invariants with bulk; Chapter 13. Partial symplectic quasi-states; Chapter 14. Construction by spectral invariant with bulk |
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14.1. Existence of the limit14.2. partial quasi-morphism property of ₁ {\frak }; 14.3. Partial symplectic quasi-state property of ̂{\frak }₁ Chapter 15. Poincaré duality and spectral invariant; 15.1. Statement of the result; 15.2. Algebraic preliminary; 15.3. Duality between Floer homologies; 15.4. Duality and Piunikhin isomorphism; 15.5. Proof of Theorem 1.1; Chapter 16. Construction of quasi-morphisms via spectral invariant with bulk; Part 4 . Spectral invariants and Lagrangian Floer theory; Chapter 17. Operator \frak ; review |
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Chapter 18. Criterion for heaviness of Lagrangian submanifolds18.1. Statement of the results; 18.2. Floer homologies of periodic Hamiltonians and of Lagrangian submanifolds; 18.3. Filtration and the map \frak _{( , )}̂{ ,\frak }; 18.4. Identity \frak _{( , )}̂{ ,\frak ,∗}∘\CP_{( ᵪ, ),∗}̂{\frak }= _{ , }*; 18.5. Heaviness of; Chapter 19. Linear independence of quasi-morphisms.; Part 5 . Applications; Chapter 20. Lagrangian Floer theory of toric fibers: review; 20.1. Toric manifolds: review; 20.2. Review of Floer cohomology of toric fiber |
| Summary |
In this paper the authors first develop various enhancements of the theory of spectral invariants of Hamiltonian Floer homology and of Entov-Polterovich theory of spectral symplectic quasi-states and quasi-morphisms by incorporating bulk deformations, i.e., deformations by ambient cycles of symplectic manifolds, of the Floer homology and quantum cohomology. Essentially the same kind of construction is independently carried out by Usher in a slightly less general context. Then the authors explore various applications of these enhancements to the symplectic topology, especially new construction |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Online resource; title from PDF title page (viewed August 27, 2019) |
| Subject |
Symplectic geometry.
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Floer homology.
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Gromov-Witten invariants.
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Grupos simplécticos
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Variedades simplécticas
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Floer homology
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Gromov-Witten invariants
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Symplectic geometry
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| Form |
Electronic book
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| Author |
Oh, Yong-Geun, 1961- author.
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Ohta, Hiroshi, 1949- author.
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Ono, Kaoru (Mathematician), author.
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| LC no. |
2019033027 |
| ISBN |
1470453258 |
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9781470453251 |
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