Knot homology via derived categories of coherent sheaves IV, coloured links

TL;DR

This paper introduces a deformation of knot homologies related to fundamental representations of sl_m, establishing their properties and a spectral sequence connecting the original and deformed homologies.

Contribution

It defines a new deformation of link homologies and proves their invariance and relation via a spectral sequence to previous homologies.

Findings

Deformed homology is isomorphic to the disjoint union of components' homologies.

Existence of a spectral sequence from original to deformed homology.

Deformation preserves key homological properties.

Abstract

We define a deformation of our earlier link homologies for fundamental representations of sl_m. The deformed homology of a link is isomorphic to the deformed homology of the disjoint union of its components. Moreover, there exists a spectral sequence starting with the old homology and converging to this deformed homology.