A Spanning Tree Model for Khovanov Homology

By S. Wehrli. 2004

58 citations recorded by the source corpus.

We show that the Khovanov complex of a connected link diagram D retracts to a subcomplex whose generators are in 2:1 correspondence with the spanning trees of the "black graph" of D. Using this result, we give a new proof of Lee's theorem on the support of Khovanov homology of alternating knots.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/1d0e081965f709ffca2da3df126f089c7c6b003b

How researchers see this paper

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In Discrete Mathematics and Combinatorics

1. John A. Baldwin
2. A. Levine
3. Lawrence P. Roberts
4. S. Wehrli

In Geometry and Topology

1. John A. Baldwin
2. A. Levine
3. Lawrence P. Roberts
4. J. Greene
5. M. Hedden
6. S. Wehrli

In Mathematical Physics

1. John A. Baldwin
2. A. Levine
3. Lawrence P. Roberts
4. M. Hedden
5. S. Wehrli

Citations in the corpus

• Spanning trees and Khovanov homology (2006, unknown): “Wehrli independently gave a spanning tree model for Khovanov homology in [13].”
• A combinatorial spanning tree model for knot Floer homology (2011, background): “Moreover, Wehrli [56] and Bloom [3] have shown that it preserves reduced Khovanov homology (with coefficients in F).”
• On knot Floer homology in double branched covers (2007, methodology): “It is shown in Appendix B that these diagrams correspond to unknots, and the diagram can be simplified in R(2) to a standard unknot diagram using only the first Reidemeister move (this is implicit in [19], but we will need the slight generalization that is proven in the appendix).”