Combinatorial Floer homology
About this Title
Vin de Silva, Joel W. Robbin and Dietmar A. Salamon
Publication: Memoirs of the American Mathematical Society
Publication Year:
2014; Volume 230, Number 1080
ISBNs: 978-0-8218-9886-4 (print); 978-1-4704-1670-6 (online)
DOI: http://dx.doi.org/10.1090/memo/1080
Published electronically: December 10, 2013
Table of Contents
Chapters
- Chapter 1. Introduction
- Chapter 2. Chains and Traces
- Chapter 3. The Maslov Index
- Chapter 4. The Simply Connected Case
- Chapter 5. The Non Simply Connected Case
- Chapter 6. Lunes and Traces
- Chapter 7. Arcs
- Chapter 8. Combinatorial Lunes
- Chapter 9. Combinatorial Floer Homology
- Chapter 10. Hearts
- Chapter 11. Invariance under Isotopy
- Chapter 12. Lunes and Holomorphic Strips
- Chapter 13. Further Developments
- Appendix A. The Space of Paths
- Appendix B. Diffeomorphisms of the Half Disc
- Appendix C. Homological Algebra
- Appendix D. Asymptotic behavior of holomorphic strips
Abstract
We define combinatorial Floer homology of a transverse pair of noncontractible nonisotopic embedded loops in an oriented -manifold without boundary, prove that it is invariant under isotopy, and prove that it is isomorphic to the original Lagrangian Floer homology. Our proof uses a formula for the Viterbo-Maslov index for a smooth lune in a -manifold.
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