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A categorification of the colored Jones polynomial at a root of unity
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abstract
There is a $p$-differential on the triply-graded Khovanov--Rozansky homology of knots and links over a field of positive characteristic $p$ that gives rise to an invariant in the homotopy category finite-dimensional $p$-complexes. A differential on triply-graded homology discovered by Cautis is compatible with the $p$-differential structure. As a consequence we get a categorification of the colored Jones polynomial evaluated at a $2p$th root of unity.
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Cited by 1 Pith paper
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An action of the Witt algebra on Khovanov-Rozansky homology
Khovanov-Rozansky gl_N link homology carries a functorial action of the positive Witt algebra, making link cobordisms equivariant maps between twisted homology groups.
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