An $\mathfrak{sl}_2$ action on link homology of T(2,k) torus links

TL;DR

This paper establishes an $rak{sl}_2$ module structure on the equivariant Khovanov-Rozansky homology of (2,k)-torus links, providing new insights into their algebraic and topological properties.

Contribution

It introduces a novel $rak{sl}_2$ action on the homology of (2,k)-torus links, extending the framework from prior work to this specific class of links.

Findings

$rak{sl}_2$ module structure explicitly determined

Enhanced understanding of link homology algebraic actions

Framework applicable to other link classes

Abstract

We determine an $\mathfrak{sl}_2$ module structure on the equivariant Khovanov-Rozansky homology of (2,k)-torus links following the framework defined in arXiv:2306.10729.