A geometric construction of colored HOMFLYPT homology

  title={A geometric construction of colored HOMFLYPT homology},
  author={B. Webster and G. Williamson},
  journal={Geometry \& Topology},
The aim of this paper is two-fold. First, we give a fully geometric description of the HOMFLYPT homology of Khovanov-Rozansky. Our method is to construct this invariant in terms of the cohomology of various sheaves on certain algebraic groups, in the same spirit as the authors' previous work on Soergel bimodules. All the differentials and gradings which appear in the construction of HOMFLYPT homology are given a geometric interpretation. In fact, with only minor modifications, we can extend… Expand