Combinatorial Floer Homology
  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. 
Vin de Silva, Joel Robbin, Dietmar Salamon
math.SG