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Article Dans Une Revue Journal of topology Année : 2014

Quantum invariants of 3-manifolds via link surgery presentations and non-semi-simple categories

Résumé

In this paper we construct invariants of 3-manifolds "á la Reshetikhin-Turaev" in the setting of non-semi-simple ribbon tensor categories. We give concrete examples of such categories which lead to a family of 3-manifold invariants indexed by the integers. We prove this family of invariants has several notable features, including: they can be computed via a set of axioms, they distinguish homotopically equivalent manifolds that the standard Reshetikhin-Turaev-Witten invariants do not, and they allow the statement of a version of the Volume Conjecture and a proof of this conjecture for an infinite class of links.

Dates et versions

hal-00680226 , version 1 (18-03-2012)

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Francesco Costantino, Nathan Geer, Bertrand Patureau-Mirand. Quantum invariants of 3-manifolds via link surgery presentations and non-semi-simple categories. Journal of topology, 2014, 7 (4), pp.1005-1053. ⟨10.1112/jtopol/jtu006⟩. ⟨hal-00680226⟩
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