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Combinatorial Spanning Tree Models for Knot Homologies
by
Adam Levine
Brandeis University
Coauthors: John Baldwin
It is well-known that the Alexander and Jones polynomials of a knot can be computed as sums of monomials corresponding to spanning trees of the Tait graph of a diagram for the knot. In this talk, I describe recent progress on extending this approach to the knot homology theories that categorify these polynomials. Specifically, Baldwin and I have constructed a complex whose generators correspond to spanning trees, whose homology is isomorphic to the knot Floer homology of the knot, and whose differential can be described completely explicitly. Roberts used a similar approach to construct a spanning tree complex for Khovanov homology. The similarities between these two constructions suggest a possible strategy for relating the two theories.
Date received: November 25, 2011
Copyright © 2011 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cbdt-28.