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

By:

Turaev, Vladimir G, 1954- [aut]

Contributor(s):

Virelizier, Alexis [oth]

Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Progress in Mathematics ; 322 | SpringerLink BücherPublisher: Cham : Birkhäuser, 2017Description: Online-Ressource (XII, 523 p, online resource)ISBN:

9783319498348

Subject(s):

Additional physical formats: 9783319498331 | Erscheint auch als: Monoidal categories and topological field theory. Druck-Ausgabe [Basel] : Birkhäuser, 2017. xii, 523 SeitenDDC classification:

512.6

MSC: MSC: *18-02 | 18D10 | 16T05 | 81T45RVK: RVK: SK 320LOC classification:

QA169

DOI: DOI: 10.1007/978-3-319-49834-8Online resources:

Summary: 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 -- IndexSummary: 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 monadsPPN: PPN: 1659351553Package identifier: Produktsigel: ZDB-2-SEB | ZDB-2-SXMS | ZDB-2-SMA

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