2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/76332We 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.19 pages, 9 figuresQuantum AlgebraOperator Algebras57M27;16W30text