PLANAR ALGEBRAS AND KUPERBERG’S 3-MANIFOLD INVARIANT

Abstract. We recapture Kuperberg’s numerical invariant of 3-manifolds as-sociated 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. 1