A combinatorial spanning tree model for knot Floer homology

Adam Levine, Brandeis

Abstract: We provide an explicit description of complex, based on spanning trees of the Tait graph of a diagram of a knot K in S^3, that computes the knot Floer homology of K. The strategy is to iterate Manolescu's unoriented skein exact sequence for knot Floer homology, using twisted coefficients in the ring of binary rational functions, to form a cube of resolutions in which the only nonzero groups correspond to the connected resolutions. This construction has intriguing similarities with recent work of Roberts and Jaeger developing an analogous construction for Khovanov homology. This is joint work with John Baldwin.