On mutation and Khovanov homology

Details On mutation and Khovanov homology On mutation and Khovanov homology

2008-01-31

arxiv.org/abs/0801.4937v2

Comm. Contemp. Math. 10 (2008), 973-992. (Special issue in memory of Xiao-Song Lin.)

Mathematics

Geometric Topology

Revised and expanded with a review of the spanning tree complex. To appear in Communications in Contemporary Mathematics, spec

Scientific paper

It is conjectured that the Khovanov homology of a knot is invariant under mutation. In this paper, we review the spanning tree complex for Khovanov homology, and reformulate this conjecture using a matroid obtained from the Tait graph (checkerboard graph) G of a knot diagram K. The spanning trees of G provide a filtration and a spectral sequence that converges to the reduced Khovanov homology of K. We show that the E_2-term of this spectral sequence is a matroid invariant and hence invariant under mutation.

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