Matrix factorizations and $gl(m|k)$-quantum invariants

TL;DR

This paper extends the construction of triply graded link homology from the $gl(m)$ algebra to the super-algebra $gl(m|k)$, broadening the algebraic framework for link invariants.

Contribution

The paper introduces a novel extension of link homology theories to super-algebras $gl(m|k)$, expanding the algebraic tools available for topological invariants.

Findings

Extended $gl(m)$ link homology to $gl(m|k)$ super-algebras

Provided new algebraic structures for link invariants

Connected super-algebra theory with geometric constructions

Abstract

In our previous papers we used the Hilbert scheme of points on $C^2$ in order to construct a triply graded link homology and its $gl(m)$ version. Here we extend the $gl(m)$ construction to super-algebras $gl(m|k)$.