On mutation and Khovanov homology

Abhijit Champanerkar; Ilya Kofman

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arXiv · 0801.4937

On mutation and Khovanov homology

Abhijit Champanerkar·Ilya Kofman

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Abstract

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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Abhijit Champanerkar, Ilya Kofman. 2008-08-12. On mutation and Khovanov homology. https://arxiv.org/abs/0801.4937

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