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On some $p$-differential graded link homologies

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arxiv 2009.06498 v2 pith:Q4VSBV3B submitted 2020-09-14 math.QA math.GT

You Qi , Joshua Sussan This is my paper · ORCID
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keywords gradeddifferentialhomologytriplycategorificationcategorycautischaracteristic
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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

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  1. Remarks on some infinitesimal symmetries of Khovanov--Rozansky homologies in finite characteristic

    math.GT 2024-12 conditional novelty 6.0 of 10

    A p-differential algebra argument reproves base point independence for characteristic-p Khovanov-Rozansky homology and yields new sl2-symmetry consequences for link homology.

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