Progress in Mathematics
© 2017
Monoidal Categories and Topological Field Theory
Authors: Turaev, Vladimir, Virelizier, Alexis
- Offers a detailed exposition accessible to students
- Provides numerous figures
- Winner of the 2016 Ferran Sunyer i Balaguer Prize
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- About this book
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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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Bibliographic Information
- Bibliographic Information
-
- Book Title
- Monoidal Categories and Topological Field Theory
- Authors
-
- Vladimir Turaev
- Alexis Virelizier
- Series Title
- Progress in Mathematics
- Series Volume
- 322
- Copyright
- 2017
- Publisher
- Birkhäuser Basel
- Copyright Holder
- Springer International Publishing AG
- eBook ISBN
- 978-3-319-49834-8
- DOI
- 10.1007/978-3-319-49834-8
- Hardcover ISBN
- 978-3-319-49833-1
- Series ISSN
- 0743-1643
- Edition Number
- 1
- Number of Pages
- XII, 523
- Topics