Monoidal Categories and Topological Field Theory

Monoidal Categories and Topological Field Theory
Author :
Publisher : Birkhäuser
Total Pages : 513
Release :
ISBN-10 : 9783319498348
ISBN-13 : 3319498347
Rating : 4/5 (347 Downloads)

Book Synopsis Monoidal Categories and Topological Field Theory by : Vladimir Turaev

Download or read book Monoidal Categories and Topological Field Theory written by Vladimir Turaev and published by Birkhäuser. This book was released on 2017-06-28 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Monoidal Categories and Topological Field Theory Related Books

Monoidal Categories and Topological Field Theory
Language: ru
Pages: 513
Authors: Vladimir Turaev
Categories: Mathematics
Type: BOOK - Published: 2017-06-28 - Publisher: Birkhäuser

GET EBOOK

This monograph is devoted to monoidal categories and their connections with 3-dimensional topological field theories. Starting with basic definitions, it procee
Tensor Categories
Language: en
Pages: 362
Authors: Pavel Etingof
Categories: Mathematics
Type: BOOK - Published: 2016-08-05 - Publisher: American Mathematical Soc.

GET EBOOK

Is there a vector space whose dimension is the golden ratio? Of course not—the golden ratio is not an integer! But this can happen for generalizations of vect
Basic Concepts of Enriched Category Theory
Language: en
Pages: 260
Authors: Gregory Maxwell Kelly
Categories: Mathematics
Type: BOOK - Published: 1982-02-18 - Publisher: CUP Archive

GET EBOOK

Category Theory in Context
Language: en
Pages: 273
Authors: Emily Riehl
Categories: Mathematics
Type: BOOK - Published: 2017-03-09 - Publisher: Courier Dover Publications

GET EBOOK

Introduction to concepts of category theory — categories, functors, natural transformations, the Yoneda lemma, limits and colimits, adjunctions, monads — re
Lectures on Tensor Categories and Modular Functors
Language: en
Pages: 232
Authors: Bojko Bakalov
Categories: Mathematics
Type: BOOK - Published: 2001 - Publisher: American Mathematical Soc.

GET EBOOK

This book gives an exposition of the relations among the following three topics: monoidal tensor categories (such as a category of representations of a quantum