Subfactors and (1+1)-dimensional TQFTs (Part 1)

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.