Thomas Kerler, Volodymyr V. Lyubashenko (auth.)3540424164, 9783540424161
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. |
Table of contents :
Introduction and Summary of Results….Pages 1-14
The Double Category of Framed, Relative 3-Cobordisms….Pages 15-95
Tangle-Categories and Presentation of Cobordisms….Pages 97-172
Isomorphism between Tangle and Cobordism Double Categories….Pages 173-215
Monoidal categories and monoidal 2-categories….Pages 217-259
Coends and construction of Hopf algebras….Pages 261-282
Construction of TQFT-Double Functors….Pages 283-311
Generalization of a modular functor….Pages 313-334
From Quantum Field Theory to Axiomatics….Pages 335-342
Double Categories and Double Functors….Pages 343-352
Thick tangles….Pages 353-368 |
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