Subfactors and (1+1)-dimensional TQFTs (Part 1)
- Date: 09/12/2006
V.S. Sunder (The Institute of Mathematical Sciences)
University of British Columbia
In this joint work with Vijay Kodiyalam (IMSc, Chennai) and Vishwambhar
Pati (ISI, Bangalore), we construct a certain 'cobordism category' D
whose morphisms are suitably decorated cobordism classes between
similarly decorated closed oriented 1-manifolds, and show that there is
essentially a bijection between (1+1-dimensional) unitary topological
quantum field theories (TQFTs) defined on D, on the one hand, and
Jones' subfactor planar algebras, on the other.
Time permitting, we shall show how this leads to an alternate
description of Kuperberg's 'quantum invariant' of 3-manifolds
associated to Hopf algebras.
Algebra Topology Seminar 2006