Combinatorial Floer Homology

Abstract

We define combinatorial Floer homology of a transverse pair of noncontractibe 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.

Final version. 125 pages, 29 figures. Memoirs of the AMS