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2007 Graphs on surfaces and Khovanov homology
Abhijit Champanerkar, Ilya Kofman, Neal Stoltzfus
Algebr. Geom. Topol. 7(3): 1531-1540 (2007). DOI: 10.2140/agt.2007.7.1531

Abstract

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.

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Abhijit Champanerkar. Ilya Kofman. Neal Stoltzfus. "Graphs on surfaces and Khovanov homology." Algebr. Geom. Topol. 7 (3) 1531 - 1540, 2007. https://doi.org/10.2140/agt.2007.7.1531

Information

Received: 27 May 2007; Accepted: 24 July 2007; Published: 2007
First available in Project Euclid: 20 December 2017

zbMATH: 1169.57004
MathSciNet: MR2366169
Digital Object Identifier: 10.2140/agt.2007.7.1531

Subjects:
Primary: 57M15, 57M25
Secondary: 05C10

Rights: Copyright © 2007 Mathematical Sciences Publishers

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