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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
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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
Add to cart
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 230; 2014; 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
  • Requests
     
     
    Review Copy – for reviewers who would like to review an AMS book
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Memoirs of the American Mathematical Society
Volume: 230; 2014; 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
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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