Colored tangle invariants and sl(2) categorification

Joshua Sussan (Medgar Evers College CUNY)

Abstract: The Reshetikhin-Turaev invariant of tangles comes from the representation theory of quantum groups. We will review this construction for the case of sl(2). Then we will introduce the notion of categorification and categorify the invariant using a category of Harish-Chandra bimodules. A specialization of this construction recovers Khovanov homology.