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

Abstract

We define a deformation of our earlier link homologies for fundamental representations of ${\mathfrak{sl}}_m$. 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.