Invariants of 3-dimensional Kirby calculus and representation theory

  • Date: 03/19/2008

Hendryk Pfeiffer, Department of Mathematics, UBC


University of British Columbia


Just as the Jones polynomial can be constructed from the Kauffman
bracket, the coloured Jones polynomia
l can be obtained from a coloured version of the Kauffman bracket,
known as `Temperley-Lieb recoupling theory'. If the bracket is eval
uated at a suitable root of unity, it not only yields an invariant of
framed tangles, but also an invariant of 3-dimensional Kirby cal
culus and thereby an invariant of (smooth) compact oriented
3-manifolds. Algebraically speaking, the root-of-unity evaluated
bracket d
efines a modular tensor category. Ever since Reshetikhin and Turaev
invented this notion, there has been the question of whether these
categories are representation categories of suitable algberas with
extra structure. In this talk, I present the answer to this questi
on and describe the algebras and their additional structure in terms of
ribbon diagrams.

Other Information: 

Algebra/Topology Seminar