Spanning trees and Khovanov homology
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- by Abhijit Champanerkar and Ilya Kofman PDF
- Proc. Amer. Math. Soc. 137 (2009), 2157-2167 Request permission
Abstract:
The Jones polynomial can be expressed in terms of spanning trees of the graph obtained by checkerboard coloring a knot diagram. We show that 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.References
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Additional Information
- Abhijit Champanerkar
- Affiliation: Department of Mathematics, College of Staten Island, The City University of New York, Staten Island, New York 10314
- Email: abhijit@math.csi.cuny.edu
- Ilya Kofman
- Affiliation: Department of Mathematics, College of Staten Island, The City University of New York, Staten Island, New York 10314
- Email: ikofman@math.csi.cuny.edu
- Received by editor(s): May 24, 2007
- Received by editor(s) in revised form: August 12, 2008
- Published electronically: February 4, 2009
- Additional Notes: The first author was supported by NSF grant DMS-0455978
The second author was supported by grants NSF DMS-0456227 and PSC-CUNY 60046-3637 - Communicated by: Alexander N. Dranishnikov
- © Copyright 2009 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 137 (2009), 2157-2167
- MSC (2000): Primary 57M25
- DOI: https://doi.org/10.1090/S0002-9939-09-09729-9
- MathSciNet review: 2480298