/ Matthew Hogancamp: Categorifying skeins in the solid torus

Matthew Hogancamp: Categorifying skeins in the solid torus

January 28, 2020
4:30 pm - 5:30 pm

Abstract: Categorifying Witten-Reshetikhin-Turaev invariants of 3-manifolds is an important problem at the interface of low-dimensional topology and higher representation theory.  In this talk I will discuss the related but much more modest goal of categorifying “skein modules” of 3-manifolds.  Specifically I will discuss in detail the case of the solid torus, which is addressed in forthcoming joint work with Eugene Gorsky and Paul Wedrich using the dg trace of categories of Soergel bimodules (in type A). The resulting theory is related to some familiar annular link homology theories, but contains essential “higher homotopical” information.