Volume 7, issue 3 (2007)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 24
Issue 6, 2971–3570
Issue 5, 2389–2970
Issue 4, 1809–2387
Issue 3, 1225–1808
Issue 2, 595–1223
Issue 1, 1–594

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1472-2739 (online)
ISSN 1472-2747 (print)
Author Index
To Appear
 
Other MSP Journals
Graphs on surfaces and Khovanov homology

Abhijit Champanerkar, Ilya Kofman and Neal Stoltzfus

Algebraic & Geometric Topology 7 (2007) 1531–1540

arXiv: math.GT/0705.3453

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.

In memory of Xiao-Song Lin

Keywords
ribbon graphs, dessin d'enfants, quasi-trees, Khovanov homology, chord diagrams
Mathematical Subject Classification 2000
Primary: 57M25, 57M15
Secondary: 05C10
References
Publication
Received: 27 May 2007
Accepted: 24 July 2007
Published: 14 November 2007
Authors
Abhijit Champanerkar
Department of Mathematics and Statistics
University of South Alabama
Mobile AL 36688
USA
{http://www.southalabama.edu/mathstat/personal_pages/achamp/}
Ilya Kofman
Department of Mathematics
College of Staten Island
City University of New York
2800 Victory Boulevard
Staten Island NY 10314
USA
{http://www.math.csi.cuny.edu/~ikofman/}
Neal Stoltzfus
Department of Mathematics
Louisiana State University
Baton Rouge LA 70803-4918
USA
{http://www.math.lsu.edu/~stoltz/}