Skip to Main content Skip to Navigation
Theses

Invariants quantiques en dimension 3 et 4, TQFTs et HQFTs

Abstract : This thesis is devoted to the study of some quantum invariants of 3-manifolds and 4-manifolds as well as their associated TQFTs and HQFTs. We establish that for all spherical category $\C$, the Turaev-Viro TQFT comes from a 1+2 dimensional HQFT which has the classifying space $B\grad$ as target space. Using the methods developed here, we give a new description of the homological Turaev-Viro invariant. Furthermore, we introduce the notion of a Picard categories which we use to link the Dijkgraff-Witten invariant to the Turaev-Viro invariant. Lastly, we construct a 4-dimensional quantum invariant and compare it to the quantum invariant defined by Crane, Kauffman and Yetter. This invariant is obtained from pairs of premodular categories which have invertible dimensions.
Document type :
Theses
Complete list of metadatas

https://tel.archives-ouvertes.fr/tel-00264048
Contributor : Jérôme Petit <>
Submitted on : Friday, March 14, 2008 - 7:37:27 AM
Last modification on : Thursday, January 11, 2018 - 6:15:40 AM
Long-term archiving on: : Friday, September 28, 2012 - 11:15:10 AM

Identifiers

  • HAL Id : tel-00264048, version 1

Citation

Jérôme Petit. Invariants quantiques en dimension 3 et 4, TQFTs et HQFTs. Mathématiques [math]. Université Montpellier II - Sciences et Techniques du Languedoc, 2007. Français. ⟨tel-00264048⟩

Share

Metrics

Record views

322

Files downloads

655