Volume 9, issue 3 (2009)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Grid diagrams and Khovanov homology

Jean-Marie Droz and Emmanuel Wagner

Algebraic & Geometric Topology 9 (2009) 1275–1297
Abstract

We explain how to compute the Jones polynomial of a link from one of its grid diagrams and we observe a connection between Bigelow’s homological definition of the Jones polynomial and Kauffman’s definition of the Jones polynomial. Consequently, we prove that the Maslov grading on the Seidel–Smith symplectic link invariant coincides with the difference between the homological grading on Khovanov homology and the Jones grading on Khovanov homology. We give some evidence for the truth of the Seidel–Smith conjecture.

Keywords
Jones polynomial, Khovanov homology, Seidel–Smith conjecture
Mathematical Subject Classification 2000
Primary: 57M27
References
Publication
Received: 14 March 2009
Revised: 6 May 2009
Accepted: 12 May 2009
Published: 1 July 2009
Authors
Jean-Marie Droz
Institut für Mathematik
Universität Zürich
Winterthurerstrasse 190
CH-8057 Zürich
Switzerland
Emmanuel Wagner
Department of Mathematics
University of Aarhus
DK-8000 Aarhus
Denmark