Grid diagrams and Khovanov homology

Details Grid diagrams and Khovanov homology Grid diagrams and Khovanov homology

2009-02-19

arxiv.org/abs/0902.3370v1

Mathematics

Geometric Topology

Scientific paper

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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