Memoirs of the American Mathematical Society 2014; 114 pp; softcover Volume: 230 ISBN10: 0821898868 ISBN13: 9780821898864 List Price: US$75 Individual Members: US$45 Institutional Members: US$60 Order Code: MEMO/230/1080
 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 ViterboMaslov index for a smooth lune in a \(2\)manifold. Table of Contents Part I. The ViterboMaslov 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
