Spanning trees and Khovanov homology
Geometric Topology
2009-04-22 v3 Combinatorics
Quantum Algebra
Abstract
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.
Cite
@article{arxiv.math/0607510,
title = {Spanning trees and Khovanov homology},
author = {Abhijit Champanerkar and Ilya Kofman},
journal= {arXiv preprint arXiv:math/0607510},
year = {2009}
}
Comments
Results in Version 2 have been split among two papers: The current Version 3 and arXiv:0801.4937[math.GT]