Legendrian knots, transverse knotsand combinatorial Floer homology

Manolescu, Ozsváth and Sarkar gave [9] an explicit description of knot Floer homology for a knot in the three-sphere as the homology groups of a chain complex CK which is described in terms of the combinatorics of a grid diagram for a knot. In fact, the constructions of [9] are done with coefficients in Z=2Z; a lift of these constructions to coefficients in Z is given by Manolescu and the authors [10], along with a purely combinatorial proof of the fact that their homology groups are knot invariants, which entirely circumvents the holomorphic description. Given a grid diagram G for the mirror m.K/ of a knot K , we refer to the resulting complex as the combinatorial chain