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Combinatorial Floer Homology
Vin de Silva, Pomona College, Claremont, CA, Joel W. Robbin, University of Wisconsin, Madison, WI, and Dietmar A. Salamon, ETH Zurich, Switzerland

Memoirs of the American Mathematical Society
2014; 114 pp; softcover
Volume: 230
ISBN-10: 0-8218-9886-8
ISBN-13: 978-0-8218-9886-4
List Price: US$75
Individual Members: US$45
Institutional Members: US$60
Order Code: MEMO/230/1080
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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
  • 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
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