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Combinatorial Floer Homology

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.