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Chromatic homology, Khovanov homology, and torsion

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Adam Lowrance (Vassar)

Abstract: Experimental computations show that the Khovanov homology of a link tends to have an abundance of torsion. However, torsion of order two appears more frequently than torsion of other orders. We give a partial explanation of this observation, at least in the first and/or last few homological gradings of Khovanov homology. There is a partial isomorphism between the Khovanov homology of a link and the chromatic polynomial categorification of a certain graph related to a diagram of the link. We show that the chromatic polynomial categorification contains only torsion of order two, and consequently, Khovanov homology can only contain torsion of order two in the gradings where the partial isomorphism is defined. This is joint work with Radmila Sazdanovic.