Geodesic
Grid diagrams and Khovanov homology
Droz, Jean-Marie1 ; Wagner, Emmanuel2
1Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
2Department of Mathematics, University of Aarhus, DK-8000 Aarhus, Denmark
Algebraic and Geometric Topology, Tome 9 (2009) no. 3, pp. 1275-1297
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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.

DOI : 10.2140/agt.2009.9.1275
Keywords: Jones polynomial, Khovanov homology, Seidel–Smith conjecture

Droz, Jean-Marie  1   ; Wagner, Emmanuel  2

1 Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
2 Department of Mathematics, University of Aarhus, DK-8000 Aarhus, Denmark 
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Droz, Jean-Marie; Wagner, Emmanuel. Grid diagrams and Khovanov homology. Algebraic and Geometric Topology, Tome 9 (2009) no. 3, pp. 1275-1297. doi: 10.2140/agt.2009.9.1275

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