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.
(source: Nielsen Book Data)
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. (source: Nielsen Book Data)