HOMFLYPT homology for links in handlebodies via type A Soergel bimodules
arXiv:1908.06878 · doi:10.4171/QT/152
Abstract
We define a triply-graded invariant of links in a genus g handlebody, generalizing the colored HOMFLYPT (co)homology of links in the 3-ball. Our main tools are the description of these links in terms of a subgroup of the classical braid group, and a family of categorical actions built from complexes of (singular) Soergel bimodules.
25 pages, lots of figures, comments welcome