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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.