Non-Semisimple Topological Quantum Field Theories for 3-Manifolds with Corners
Thomas Kerler, Volodymyr V. Lyubashenko
378 pages, parution le 29/10/2001
Résumé
This book presents the (to date) most general approach to
combinatorial constructions of topological quantum field
theories (TQFTs) in three dimensions. The authors describe
extended TQFTs as double functors between two naturally
defined double categories: one of topological nature, made
of 3-manifolds with corners, the other of algebraic nature,
made of linear categories, functors, vector spaces and
maps. Atiyah's conventional notion of TQFTs as well as the
notion of modular functor from axiomatic conformal field
theory are unified in this concept. A large class of such
extended modular catergory is constructed, assigning a
double functor to every abelian modular category, which
does not have to be semisimple.
Contents
- Introduction and summary of results.
- The double category of framed, relative 3-cobordisms.
- Tangle
- categories and presentation of cobordisms.
- Isomorphism between tangle and cobordism categories.
- Monoidal categories and monoidal 2-categories.
- Coends and construction of Hopf algebras.
- Construction of TQFT
- Double Functors.
- Generalization of modular functor.
- A: From quantum field theory of axiomatics.
- B: Double categories and double functors.
- C: Thick tangles.
Caractéristiques techniques
| PAPIER | |
| Éditeur(s) | Springer |
| Auteur(s) | Thomas Kerler, Volodymyr V. Lyubashenko |
| Parution | 29/10/2001 |
| Nb. de pages | 378 |
| Format | 15,5 x 23,5 |
| Couverture | Broché |
| Poids | 548g |
| Intérieur | Noir et Blanc |
| EAN13 | 9783540424161 |
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