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Combinatorial Floer Homology
| eBook 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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Combinatorial Floer Homology
| eBook 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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Book DetailsMemoirs of the American Mathematical SocietyVolume: 230; 2014; 114 ppMSC: 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.
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Table of Contents
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Chapters
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1. Introduction
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Part I. The Viterbo–Maslov Index
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2. Chains and Traces
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3. The Maslov Index
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4. The Simply Connected Case
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5. The Non Simply Connected Case
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Part II. Combinatorial Lunes
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6. Lunes and Traces
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7. Arcs
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8. Combinatorial Lunes
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Part III. Floer Homology
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9. Combinatorial Floer Homology
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10. Hearts
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11. Invariance under Isotopy
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12. Lunes and Holomorphic Strips
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13. Further Developments
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Appendices
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A. The Space of Paths
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B. Diffeomorphisms of the Half Disc
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C. Homological Algebra
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D. Asymptotic behavior of holomorphic strips
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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 publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.