Combinatorial Floer Homology

ISBN-13: 9780821898864 / Angielski

Vin de Silva;Joel W. Robbin;Dietmar Salamon

Opis

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.

Spis treści

• 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