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Grid diagrams and Khovanov homology


Droz, J-M; Wagner, E (2009). Grid diagrams and Khovanov homology. Algebraic & Geometric Topology, 9(3):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.

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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:Jones polynomial, Khovanov homology, Seidel–Smith conjecture
Language:English
Date:2009
Deposited On:14 Apr 2010 06:44
Last Modified:17 Feb 2018 23:10
Publisher:Mathematical Sciences Publishers
ISSN:1472-2739
OA Status:Hybrid
Publisher DOI:https://doi.org/10.2140/agt.2009.9.1275

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