Combinatorial Floer Homology

Vin de Silva, Joel W. Robbin, Dietmar A. Salamon (Autoren)

Buch | Softcover

114 Seiten

2014
American Mathematical Society (Verlag)
978-0-8218-9886-4 (ISBN)

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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 Viterbo-Maslov index for a smooth lune in a 2 -manifold.

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

Reihe/Serie	Memoirs of the American Mathematical Society
Verlagsort	Providence
Sprache	englisch
Maße	178 x 254 mm
Gewicht	200 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-10	0-8218-9886-8 / 0821898868
ISBN-13	978-0-8218-9886-4 / 9780821898864
Zustand	Neuware