Grid diagrams and Khovanov homology

Droz, Jean-Marie; Wagner, Emmanuel

doi:10.2140/agt.2009.9.1275

Download this article
	For screen
	For printing

Recent 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

Grid diagrams and Khovanov homology

Jean-Marie Droz and Emmanuel Wagner

Algebraic & Geometric Topology 9 (2009) 1275–1297

DOI: 10.2140/agt.2009.9.1275

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

Volume 9, issue 3 (2009)