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.
Reihe
Sprache
Verlagsort
Zielgruppe
Maße
Höhe: 254 mm
Breite: 178 mm
Gewicht
ISBN-13
978-0-8218-9886-4 (9780821898864)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
Vin de Silva, Pomona College, Claremont, CA.
Joel W. Robbin, University of Wisconsin, Madison, WI.
Dietmar A. Salamon, ETH Zurich, Switzerland.
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
