Monoidal Categories and Topological Field Theory: 322 (Progress in Mathematics, 322) - Image 1

£128.20

Birkhauser Monoidal Categories and Topological Field Theory: 322 (Progress in Mathematics, 322)

Name: Monoidal Categories and Topological Field Theory: 322 (Progress in Mathematics, 322)
Brand: Birkhauser
Price: 128.2 GBP
Availability: InStock

Algebra

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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. Review “The book gives a self-contained account of the algebraic construction of TQFTs including all required background on the theory of monoidal categories. As such, it appears to be unique in the literature. Material otherwise only accessible through various journal articles, and partly only published in preprints, has been combined into a single well-written and accessible account of the theory. The book combines decades of research into a single text, bringing the reader from the basics to the forefront of research.” (Robert Laugwitz, Mathematical Reviews, July, 2018) From the Back Cover 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 Specifications

Brand: Birkhauser
Format: Paperback
ASIN: 3319842501
Category: Books > Subjects > Science, Nature & Maths > Mathematics > Algebra
Domain: Amazon UK
Release Date: 01 August 2018
Listed Since: 31 July 2018

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Birkhauser Monoidal Categories and Topological Field Theory: 322 (Progress in Mathematics, 322)

About as cheap as it gets. The only time it was cheaper was 11 months ago.

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