  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.
