Combinatorial Floer homology

Author(s)

• De Silva, Vin
• Robbin, Joel W.
• Salamon, D. (Dietmar)

Bibliographic Information

Combinatorial Floer homology

Vin de Silva, Joel W. Robbin, Dietmar A. Salamon

（Memoirs of the American Mathematical Society, no. 1080）

American Mathematical Society, 2014, c2013

Note

Includes bibliographical references (p. 111-112) and index

"Volume 230, number 1080 (second of 5 numbers), July 2014"

Description and Table of Contents

Description

The authors define combinatorial Floer homology of a transverse pair of noncontractible nonisotopic embedded loops in an oriented 2-manifold without boundary, prove that it is invariant under isotopy, and prove that it is isomorphic to the original Lagrangian Floer homology. Their proof uses a formula for the Viterbo-Maslov index for a smooth lune in a 2-manifold.

Table of Contents

Introduction Part I. The Viterbo-Maslov Index: Chains and traces The Maslov index The simply connected case The Non simply connected case Part II. Combinatorial Lunes: Lunes and traces Arcs Combinatorial lunes Part III. Floer Homology: Combinatorial Floer homology Hearts Invariance under isotopy Lunes and holomorphic strips Further developments Appendices: Appendix A. The space of paths Appendix B. Diffeomorphisms of the half disc Appendix C. Homological algebra Appendix D. Asymptotic behavior of holomorphic strips Bibliography Index

by "Nielsen BookData"

Details

• NCID: BB15904801
• ISBN:
  • 9780821898864
• LCCN: 2014008204
• Country Code: us
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Providence, R. I.
• Pages/Volumes: v, 114 p.
• Size: 26cm
• Classification:
  • LCC : QA665
  • DC23 : 516.3/6
• Subject Headings:
  • LCSH : Floer homology
• Parent Bibliography ID:
  • BA00035927