Authors:
- Offers a detailed exposition accessible to students
- Provides numerous figures
- Winner of the 2016 Ferran Sunyer i Balaguer Prize
Part of the book series: Progress in Mathematics (PM, volume 322)
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Table of contents (17 chapters)
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Front Matter
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Monoidal Categories
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Front Matter
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Hopf Algebras and Monads
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Front Matter
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State Sum Topological Field Theory
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Front Matter
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Graph Topological Field Theory
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Front Matter
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About this book
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 tothe 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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Authors and Affiliations
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Department of Mathematics, Indiana University, Bloomington, USA
Vladimir Turaev
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Laboratoire Paul Painlevé, Université de Lille, Villeneuve d'Ascq Cedex, France
Alexis Virelizier
Bibliographic Information
Book Title: Monoidal Categories and Topological Field Theory
Authors: Vladimir Turaev, Alexis Virelizier
Series Title: Progress in Mathematics
DOI: https://doi.org/10.1007/978-3-319-49834-8
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG 2017
Hardcover ISBN: 978-3-319-49833-1Published: 07 July 2017
Softcover ISBN: 978-3-319-84250-9Published: 01 August 2018
eBook ISBN: 978-3-319-49834-8Published: 28 June 2017
Series ISSN: 0743-1643
Series E-ISSN: 2296-505X
Edition Number: 1
Number of Pages: XII, 523
Topics: Category Theory, Homological Algebra, Manifolds and Cell Complexes (incl. Diff.Topology)