Journal of Operator Theory

Volume 63, Issue 1, Winter 2010 pp. 159-180.

Planar algebras and Kuperberg's 3-manifold invariant

Authors: Vijay Kodiyalam (1) and V. S. Sunder (2)
Author institution: (1) The Institute of Mathematical Sciences, Chennai, 600113, India
(2) The Institute of Mathematical Sciences, Chennai, 600113, India

Summary: 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.

Keywords: Hopf algebras, planar algebras, 3-manifold invariants

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