HOMFLYPT homology for links in handlebodies

(Joint work with David Rose)

It is a classical question what kind of low-dimensional topology is encoded in Artin--Tits groups with the example of braids in three-space associated to Coxeter type A. An answer would give rise to a HOMFLYPT-type invariant, with the classical HOMFLYPT polynomial associated to Coxeter type A as a key example.

In this talk I explain the difficulties which arise trying to answer this question and what we can do at the moment as a roundabout to produce HOMFLYPT invariants for links in handlebodies.