Non-semisimple Extended Topological Quantum Field Theories - Couverture souple

Renzi, Marco De

Couverture souple

ISBN 10 : 1470452693 ISBN 13 : 9781470452698

Editeur : American Mathematical Society, 2022

Synopsis

"We develop the general theory for the construction of Extended Topological Quantum Field Theories (ETQFTs) associated with the Costantino-Geer-Patureau quantum invariants of closed 3-manifolds. In order to do so, we introduce relative modular categories, a class of ribbon categories which are modeled on representations of unrolled quantum groups, and which can be thought of as a non-semisimple ogue to modular categories. Our approach exploits a 2-categorical version of the universal construction introduced by Blanchet, Habegger, Masbaum, and Vogel. The 1+1+1-EQFTs thus obtained are realized by symmetric monoidal 2-functors which are defined over non-rigid 2-categories of admissible cobordisms decorated with colored ribbon graphs and cohomology classes, and which take values in 2- categories of complete graded linear categories. In partiar, our construction extends the family of graded 2+1-TQFTs defined for the unrolled version of quantum sl2 by Blanchet, Costantino, Geer, and Patureau to a new family of graded ETQFTs. The non-semisimplicity of the theory is witnessed by the presence of non-semisimple graded linear categories associated with critical 1-manifolds"--

A propos du livre

À propos de l'auteur

Marco De Renzi, Universite Paris Diderot, France.

Détails de l'édition

• Éditeur: American Mathematical Society
• Date d'édition: 2022
• Langue: anglais
• ISBN 10: 1470452693
• ISBN 13: 9781470452698
• Reliure: Broché
• Nombre de pages: 161
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible