Subfactors and 1+1-dimensional TQFTs
  We construct a certain `cobordism category' ${\cal D}$ 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 ${\cal D}$, on the one hand, and Jones' subfactor planar algebras, on the other. 
Vijay Kodiyalam, Vishwambhar Pati and V.S. Sunder