 |
 |
 |
 |
|
|
|
|
| HAL: hal-00680226, version 1 |
| arXiv: 1202.3553 |
| Detailed view |  Export this paper |
 |
|
|
| Quantum invariants of 3-manifolds via link surgery presentations and non-semi-simple categories |
|
|
| Francesco Costantino 1Nathan Geer |
|
|
| (2012-02-16) |
|
|
|
| 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: | Institut de Recherche Mathématique Avancée (IRMA) |
|
|
|
CNRS : UMR7501 – Université de Strasbourg |
|
|
| 2: | Laboratoire de Mathématiques et Applications des Mathématiques, EA 3885 (LMAM) |
|
|
|
Université de Bretagne Sud |
|
|
|
|
|
|
|
|
|
| Subject | : | Mathematics/Geometric Topology Mathematics/Quantum Algebra |
|
|
| Fulltext link: |
|
| http://fr.arXiv.org/abs/1202.3553 |
| hal-00680226, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00680226 | |
| oai:hal.archives-ouvertes.fr:hal-00680226 | |
| From: Bertrand Patureau-Mirand | |
| Submitted on: Sunday, 18 March 2012 17:54:22 | |
| Updated on: Sunday, 18 March 2012 17:54:22 | |
