Combinatorial Floer homology
著者
書誌事項
Combinatorial Floer homology
(Memoirs of the American Mathematical Society, no. 1080)
American Mathematical Society, 2014, c2013
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注記
Includes bibliographical references (p. 111-112) and index
"Volume 230, number 1080 (second of 5 numbers), July 2014"
内容説明・目次
内容説明
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.
目次
Introduction
Part I. The Viterbo-Maslov
Index: Chains and traces
The Maslov index
The simply connected case
The Non simply connected case
Part II. Combinatorial Lunes: Lunes and traces
Arcs Combinatorial lunes
Part III. Floer Homology: Combinatorial Floer homology
Hearts Invariance under isotopy
Lunes and holomorphic strips
Further developments
Appendices: Appendix A.
The space of paths
Appendix B. Diffeomorphisms of the half disc
Appendix C. Homological algebra
Appendix D. Asymptotic behavior of holomorphic strips
Bibliography
Index
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