Combinatorial Floer Homology
Will be published approx. on 30. June 2014
Book
Paperback/Softback
114 pages
978-0-8218-9886-4 (ISBN)
Description
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.
More details
Series
Language
English
Place of publication
Providence
United States
Target group
Professional and scholarly
Dimensions
Height: 254 mm
Width: 178 mm
Weight
200 gr
ISBN-13
978-0-8218-9886-4 (9780821898864)
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Schweitzer Classification
Persons
Vin de Silva, Pomona College, Claremont, CA.
Joel W. Robbin, University of Wisconsin, Madison, WI.
Dietmar A. Salamon, ETH Zurich, Switzerland.
Joel W. Robbin, University of Wisconsin, Madison, WI.
Dietmar A. Salamon, ETH Zurich, Switzerland.
Content
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
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