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Monoidal Categories and Topological Field Theory / / by Vladimir Turaev, Alexis Virelizier



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Autore: Turaev Vladimir Visualizza persona
Titolo: Monoidal Categories and Topological Field Theory / / by Vladimir Turaev, Alexis Virelizier Visualizza cluster
Pubblicazione: Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2017
Edizione: 1st ed. 2017.
Descrizione fisica: 1 online resource (523 pages)
Disciplina: 512.55
Soggetto topico: Category theory (Mathematics)
Homological algebra
Manifolds (Mathematics)
Complex manifolds
Category Theory, Homological Algebra
Manifolds and Cell Complexes (incl. Diff.Topology)
Persona (resp. second.): VirelizierAlexis
Nota di bibliografia: Includes bibliographical references and index.
Nota di contenuto: 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.
Sommario/riassunto: 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.
Titolo autorizzato: Monoidal Categories and Topological Field Theory  Visualizza cluster
ISBN: 3-319-49834-7
Formato: Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione: Inglese
Record Nr.: 9910254282003321
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Serie: Progress in Mathematics, . 0743-1643 ; ; 322