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ON MUTATION AND KHOVANOV HOMOLOGY
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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 E2-term of this spectral sequence is a matroid invariant and hence invariant under mutation.
World Scientific Pub Co Pte Ltd
Title: ON MUTATION AND KHOVANOV HOMOLOGY
Description:
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 E2-term of this spectral sequence is a matroid invariant and hence invariant under mutation.
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