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Involutory Hopf algebras and 3-manifold invariants. (English) Zbl 0726.57016
Author’s summary: “We establish a 3-manifold invariant for each finite- dimensional, involutory Hopf algebra. If the Hopf algebra is a group algebra G, the invariant counts homomorphisms from the fundamental group of the manifold to G. The invariant can be viewed as a state model on a Heegaard diagram or a triangulation of the manifold. The computation of the invariant involves tensor products and contractions of the structure tensors of the algebra. We show that every formal expression involving these tensors corresponds to a unique 3-manifold modulo a well-understood equivalence. This raises the possibility of an algorithm which can determine whether two given 3-manifolds are homeomorphic.”
Reviewer: C.Kearton (Durham)

MSC:
57N10 Topology of general \(3\)-manifolds (MSC2010)
57T05 Hopf algebras (aspects of homology and homotopy of topological groups)
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