# 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.
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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

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• 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⟩

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