On some $p$-differential graded link homologies

Abstract

We show that the triply graded Khovanov-Rozansky homology of knots and links over a field of positive odd characteristic $p$ descends to an invariant in the homotopy category finite-dimensional $p$-complexes. A $p$-extended differential on the triply graded homology discovered by Cautis is compatible with the $p$-DG structure. As a consequence we get a categorification of the Jones polynomial evaluated at an odd prime root of unity

arXiv comment53 pages. V2 contains corrections from referee reports. Comments welcome

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• A categorification of the colored Jones polynomial at a root of unity
• On some $p$-differential graded link homologies II
• Enhanced nilHecke algebras and baby Verma modules
• Symmetries of ${\mathfrak{gl}}_N$-foams