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

TL;DR

This paper provides a new proof of base point independence in Khovanov--Rozansky homology over finite characteristic fields and explores additional symmetries in $rak{gl}(p)$-homology.

Contribution

It introduces a novel proof for a key property of Khovanov--Rozansky homology in characteristic p and discusses new symmetries in $rak{gl}(p)$-homology.

Findings

Proof of base point independence in characteristic p

Identification of new symmetries in $rak{gl}(p)$-homology

Enhanced understanding of infinitesimal symmetries in homology theories

Abstract

We give a new proof of a theorem due to Shumakovitch and Wang on base point independence of Khovanov--Rozansky homology in characteristic $p$. Some further symmetries of $\mathfrak{gl}(p)$-homology in characteristic $p$ are also discussed.