Monoidal Categories and Topological Field Theory

Vladimir turaev (author)|alexis virelizier (author) - Collection Yellow Sale 2023

523 pages, parution le 06/07/2017

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Résumé

Introduction.- Part I: Monoidal Categories.- Part 2: Hopf Algebras and Monads.- Part 3: State Sum Topological Field Theory.- Part 4: Graph Topological Field Theory.- Appendices.- Bibliography.- Index.

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.

1st Edition 2017th editionQA169Categories (Mathematics)|Topological fields.1SwitzerlandCham9783319498348|9783319498355Vladimir Turaev, Alexis Virelizier.Progress in Mathematics322

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Vladimir turaev (author)\|alexis virelizier (author)
Collection	Yellow Sale 2023
Parution	06/07/2017
Nb. de pages	523
Format	155 x 235
Poids	961g
EAN13	9783319498331