Author Description

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.