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

Francesco Costantino; Nathan Geer; Bertrand Patureau-Mirand

doi:10.1112/jtopol/jtu006

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arXiv · 1202.3553

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

Francesco Costantino·Nathan Geer·Bertrand Patureau-Mirand

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Abstract

In this paper we construct invariants of 3-manifolds "\`a 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.

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Francesco Costantino, Nathan Geer, Bertrand Patureau-Mirand. 2012-02-16. Quantum invariants of 3-manifolds via link surgery presentations and non-semi-simple categories. https://doi.org/10.1112/jtopol%2Fjtu006

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