An Algebra Structure for the stable Khovanov homology of torus links

TL;DR

This paper introduces a new algebraic structure on the stable reduced Khovanov homology of torus links, providing explicit descriptions for small cases and applications to link homology computations.

Contribution

It defines a bi-graded algebra structure on stable Khovanov homology of torus links and explicitly describes these algebras for p=2,3,4.

Findings

Explicit algebra structures for p=2,3,4

Computed homology for specific link families

Established a lower bound for the width of 4-stranded torus link homology

Abstract

The family of negative torus links $T_{p,q}$ over a fixed number of strands $p$ admits a stable limit in reduced Khovanov homology as $q$ grows to infinity. In this paper, we endow this stable space with a bi-graded commutative algebra structure. We describe these algebras explicitly for $p=2,3,4$. As an application, we compute the homology of two families of links, and produce a lower bound for the width of the homology of any $4$-stranded torus link.