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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
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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
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
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