Quantum invariants of 3-manifolds via link surgery presentations and non-semi-simple categories
Geometric Topology
2017-05-17 v3 Quantum Algebra
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.
Keywords
Cite
@article{arxiv.1202.3553,
title = {Quantum invariants of 3-manifolds via link surgery presentations and non-semi-simple categories},
author = {Francesco Costantino and Nathan Geer and Bertrand Patureau-Mirand},
journal= {arXiv preprint arXiv:1202.3553},
year = {2017}
}
Comments
46 pages, 45 figures, new introduction, some misprints corrected and an example detailed. An appendix added to correct a proof