Séminaires : Séminaire de Topologie

Topological invariants of knots and 3-manifolds can be constructed either using tools from algebraic topology (classical invariants) or via the representation theory of certain Hopf algebras (quantum invariants). In this talk we will discuss another approach, due to G. Kuperberg, that associates (quantum) invariants to closed 3-manifolds directly from an arbitrary finite dimensional Hopf algebra. We will show that, at least when the Hopf algebra is involutive, this approach can be extended to sutured 3-manifolds, a common generalization of closed 3-manifolds, knot complements and Seifert surface complements. When specialized to an exterior Hopf algebra, we show that this extension recovers a classical invariant: the Reidemeister torsion and its twisted versions.