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Combinatorial Floer Homology
 
Vin de Silva Pomona College, Claremont, CA
Joel W. Robbin University of Wisconsin, Madison, WI
Dietmar A. Salamon ETH Zurich, Zurich, Switzerland
Front Cover for Combinatorial Floer Homology
Available Formats:
Electronic ISBN: 978-1-4704-1670-6
Product Code: MEMO/230/1080.E
List Price: $75.00
MAA Member Price: $67.50
AMS Member Price: $45.00
Front Cover for Combinatorial Floer Homology
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  • Front Cover for Combinatorial Floer Homology
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Combinatorial Floer Homology
Vin de Silva Pomona College, Claremont, CA
Joel W. Robbin University of Wisconsin, Madison, WI
Dietmar A. Salamon ETH Zurich, Zurich, Switzerland
Available Formats:
Electronic ISBN:  978-1-4704-1670-6
Product Code:  MEMO/230/1080.E
List Price: $75.00
MAA Member Price: $67.50
AMS Member Price: $45.00
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 2302014; 114 pp
    MSC: Primary 57;

    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
     
     
    • Chapters
    • 1. Introduction
    • Part I. The Viterbo–Maslov Index
    • 2. Chains and Traces
    • 3. The Maslov Index
    • 4. The Simply Connected Case
    • 5. The Non Simply Connected Case
    • Part II. Combinatorial Lunes
    • 6. Lunes and Traces
    • 7. Arcs
    • 8. Combinatorial Lunes
    • Part III. Floer Homology
    • 9. Combinatorial Floer Homology
    • 10. Hearts
    • 11. Invariance under Isotopy
    • 12. Lunes and Holomorphic Strips
    • 13. Further Developments
    • Appendices
    • A. The Space of Paths
    • B. Diffeomorphisms of the Half Disc
    • C. Homological Algebra
    • D. Asymptotic behavior of holomorphic strips
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Volume: 2302014; 114 pp
MSC: Primary 57;

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.

  • Chapters
  • 1. Introduction
  • Part I. The Viterbo–Maslov Index
  • 2. Chains and Traces
  • 3. The Maslov Index
  • 4. The Simply Connected Case
  • 5. The Non Simply Connected Case
  • Part II. Combinatorial Lunes
  • 6. Lunes and Traces
  • 7. Arcs
  • 8. Combinatorial Lunes
  • Part III. Floer Homology
  • 9. Combinatorial Floer Homology
  • 10. Hearts
  • 11. Invariance under Isotopy
  • 12. Lunes and Holomorphic Strips
  • 13. Further Developments
  • Appendices
  • A. The Space of Paths
  • B. Diffeomorphisms of the Half Disc
  • C. Homological Algebra
  • D. Asymptotic behavior of holomorphic strips
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