hal-00680226, version 1
Quantum invariants of 3-manifolds via link surgery presentations and non-semi-simple categories
(16/02/2012)
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.
- 1 :
- CNRS : UMR7501 – Université de Strasbourg
- 2 :
- Université de Bretagne Sud
- Domaine : Mathématiques/Topologie géométrique
Mathématiques/Algèbres quantiques - Commentaire : 42 pages – 42 figures
- hal-00680226, version 1
- http://hal.archives-ouvertes.fr/hal-00680226
- oai:hal.archives-ouvertes.fr:hal-00680226
- Contributeur :
- Soumis le : Dimanche 18 Mars 2012, 17:54:22
- Dernière modification le : Dimanche 18 Mars 2012, 17:54:22
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