Graphs on surfaces and Khovanov homology
By Abhijit Champanerkar, Ilya Kofman, Neal W. Stoltzfus. 2007
50 citations recorded by the source corpus.
Oriented ribbon graphs (dessins d’enfant) are graphs embedded in oriented surfaces. A quasi-tree of a ribbon graph is a spanning subgraph with one face, which is described by an ordered chord diagram. We show that for any link diagram L, there is an associated ribbon graph whose quasi-trees correspond bijectively to spanning trees of the graph obtained by checkerboard coloring L. This correspondence preserves the bigrading used for the spanning tree model of Khovanov homology, whose Euler characteristic is the Jones polynomial of L. Thus, Khovanov homology can be expressed in terms of ribbon graphs, with generators given by ordered chord diagrams.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/9b1e67896f6623a209ac4bb5aae3670771998e07
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In Discrete Mathematics and Combinatorics
- Ilya Kofman
- Abhijit Champanerkar
- Joanna A. Ellis-Monaghan
- Iain Moffatt
- Lawrence P. Roberts
- John A. Baldwin
In Geometry and Topology
- Ilya Kofman
- Abhijit Champanerkar
- Joanna A. Ellis-Monaghan
- Iain Moffatt
- J. Greene
- Lawrence P. Roberts
- John A. Baldwin
In Mathematical Physics
- Ilya Kofman
- Abhijit Champanerkar
- Joanna A. Ellis-Monaghan
- Iain Moffatt
- Lawrence P. Roberts
- John A. Baldwin
Citations in the corpus
- Twisting quasi-alternating links (2007, methodology): “Finally, the Turaev genus plus two bounds the homological thickness for both Khovanov homology and knot Floer homology [16, 5, 13].”
- Twisted duality for embedded graphs (2009, background): “From [24] (see also [14, 15, 86]), a quasi-tree is an embedded graph with exactly one boundary component (or face).”
- On knot Floer width and Turaev genus (2007, unknown): “G T ] 5 S ep 2”
- Spanning trees and Khovanov homology (2006, result): “pport of Khovanov homology for alternating and k-almost alternating links obtained respectively by Lee [5] and Asaeda, Przytycki [1]. We proved a more general result in terms of ribbon graph genus in [2]. Another proof also appeared in Manturov [6]. Theorem 8. (i) The Khovanov homology of a non-spli”