Spanning trees and Khovanov homology

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The Jones polynomial can be expressed in terms of spanning trees of the graph obtained by checkerboard coloring a knot diagram. We show there exists a complex generated by these spanning trees whose homology is the reduced Khovanov homology. The spanning trees provide a filtration on the reduced Khovanov complex and a spectral sequence that converges to its homology. For alternating links, all differentials on the spanning tree complex are zero and the reduced Khovanov homology is determined by the Jones polynomial and signature. We prove some analogous theorems for (unreduced) Khovanov homology.
Results in Version 2 have been split among two papers: The current Version 3 and arXiv:0801.4937[math.GT]

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Geometric Topology, Combinatorics, Quantum Algebra

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http://salesiana.dossiersoluciones.com/handle/123456789/227779

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0607510
 http://arxiv.org/abs/math/0607510
 Proc. Amer. Math. Soc., 137 (2009), 2157-2167.

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arXiv