Knot complements, series invariants and Lie superalgebra

Abstract: Inspired by a categorification of a numerical invariant of 3-manifolds, series invariants for closed manifolds and for knot complements were introduced. This in turn motivated an extension of the series invariant of the former case to Lie superalgebras. It was recently generalized to knot complements. In this talk, we review the original series invariants and introduce the recent generalization and explore its properties and examples.