Vladimir Turaev

(Author)

Monoidal Categories and Topological Field Theory (2017)Hardcover - 2017, 7 July 2017

Monoidal Categories and Topological Field Theory (2017)
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Part of Series
Progress in Mathematics
Print Length
523 pages
Language
English
Publisher
Birkhauser
Date Published
7 Jul 2017
ISBN-10
3319498339
ISBN-13
9783319498331

Description

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.

Product Details

Authors:
Vladimir TuraevAlexis Virelizier
Book Edition:
2017
Book Format:
Hardcover
Country of Origin:
NL
Date Published:
7 July 2017
Dimensions:
23.39 x 15.6 x 3.02 cm
ISBN-10:
3319498339
ISBN-13:
9783319498331
Language:
English
Location:
Cham
Pages:
523
Publisher:
Weight:
920.79 gm

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