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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 Click above image for expanded view 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.

• 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
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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
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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