A categorification of the colored Jones polynomial at a root of unity

2021/11/25 by Qi, You, Robert, Louis-Hadrien, Sussan, Joshua +1 · 1 citation
#18G99 #57M27 #FOS: Mathematics #Geometric Topology (math.GT) #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2111.13195

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 2pth root of unity.

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