Table of contents
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 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.
- Book Title Monoidal Categories and Topological Field Theory
- Series Title Progress in Mathematics
- Series Abbreviated Title Progress in Mathematics(Birkhäuser)
- DOI https://doi.org/10.1007/978-3-319-49834-8
- Copyright Information Springer International Publishing AG 2017
- Publisher Name Birkhäuser, Cham
- eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
- Hardcover ISBN 978-3-319-49833-1
- Softcover ISBN 978-3-319-84250-9
- eBook ISBN 978-3-319-49834-8
- Series ISSN 0743-1643
- Series E-ISSN 2296-505X
- Edition Number 1
- Number of Pages XII, 523
- Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
Category Theory, Homological Algebra
Manifolds and Cell Complexes (incl. Diff.Topology)
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