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

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.

arXiv comment72 pages, many figures. Comments welcome!

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• Symmetries of ${\mathfrak{gl}}_N$-foams