Electronic ISBN:  9781470416706 
Product Code:  MEMO/230/1080.E 
List Price:  $75.00 
MAA Member Price:  $67.50 
AMS Member Price:  $45.00 

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 ViterboMaslov 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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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 ViterboMaslov 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