Planar algebras and Kuperberg's 3-manifold invariant
  We recapture Kuperberg's numerical invariant of 3-manifolds associated to a semisimple and cosemisimple Hopf algebra through a `planar algebra construction'. A result of possibly independent interest, used during the proof, which relates duality in planar graphs and Hopf algebras, is the subject of a final section. 
Vijay Kodiyalam and V.S. Sunder