Monoidal Categories and Topological Field Theory
| Autor: | Vladimir Turaev, Alexis Virelizier |
|---|---|
| EAN: | 9783319498348 |
| eBook Format: | |
| Sprache: | Englisch |
| Produktart: | eBook |
| Veröffentlichungsdatum: | 28.06.2017 |
| Kategorie: | |
| Schlagworte: | 3-manifold invariants Hopf algebras Hopf monads monoidal categories state sums topological quantum field theory |
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This monograph is devoted to monoidal categories and their connections with 3-dimensional topological field theories. Starting with basic definitions, it proceeds to the forefront of current research.
Part 1 introduces monoidal categories and several of their classes, including rigid, pivotal, spherical, fusion, braided, and modular categories. It then presents deep theorems of Müger on the center of a pivotal fusion category. These theorems are proved in Part 2 using the theory of Hopf monads. In Part 3 the authors define the notion of a topological quantum field theory (TQFT) and construct a Turaev-Viro-type 3-dimensional state sum TQFT from a spherical fusion category. Lastly, in Part 4 this construction is extended to 3-manifolds with colored ribbon graphs, yielding a so-called graph TQFT (and, consequently, a 3-2-1 extended TQFT). The authors then prove the main result of the monograph: the state sum graph TQFT derived from any spherical fusion category is isomorphic to the Reshetikhin-Turaev surgery graph TQFT derived from the center of that category.The book is of interest to researchers and students studying topological field theory, monoidal categories, Hopf algebras and Hopf monads.
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