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

By Francesco Costantino, Nathan Geer, Bertrand Patureau-Mirand. 2012

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In this paper, we construct invariants of 3‐manifolds ‘à la Reshetikhin–Turaev ’ in the setting of non‐semi‐simple ribbon tensor categories. We give concrete examples of such categories that lead to a family of 3‐manifold invariants indexed by the integers. We prove that 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 Witten–Reshetikhin–Turaev 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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f5c9b989b325cf73d1a6953272fe553735b7d60f