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Spectral invariants with bulk, quasi-morphisms and Lagrangian floer theory /
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 symplect...
| Call Number: | Libro Electrónico |
|---|---|
| Main Authors: | , , , |
| Format: | Electronic eBook |
| Language: | Inglés |
| Published: |
Providence, RI :
American Mathematical Society,
2019.
|
| Series: | Memoirs of the American Mathematical Society ;
no. 1254. |
| Subjects: | |
| Online Access: | Texto completo |
Table of 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
- 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
- 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
- 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