Overview

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.

Full Product Details

Author:   Vin de Silva ,  Joel W. Robbin ,  Dietmar A. Salamon
Publisher:   American Mathematical Society
Imprint:   American Mathematical Society
Volume:   No. 230/1080
Weight:   0.200kg
ISBN:  

9780821898864

ISBN 10:   0821898868
Pages:   114
Publication Date:   30 June 2014
Audience:   Professional and scholarly ,  Professional and scholarly ,  Professional & Vocational ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Temporarily unavailable  
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Table of Contents

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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Author Information

Vin de Silva, Pomona College, Claremont, CA. Joel W. Robbin, University of Wisconsin, Madison, WI. Dietmar A. Salamon, ETH Zurich, Switzerland.

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