Monoidal Categories and Topological Field Theory (Progress in Mathematics #322) (Hardcover)

Monoidal Categories and Topological Field Theory (Progress in Mathematics #322) By Vladimir Turaev, Alexis Virelizier Cover Image

Monoidal Categories and Topological Field Theory (Progress in Mathematics #322) (Hardcover)


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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 M ger 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.

Product Details ISBN: 9783319498331
ISBN-10: 3319498339
Publisher: Birkhauser
Publication Date: July 7th, 2017
Pages: 523
Language: English
Series: Progress in Mathematics