Monoidal Categories and Topological Field Theory

Autor: Vladimir Turaev, Alexis Virelizier

Limbă:

Legare: Carte broșată

Editura: Birkhauser Verlag AG

Disponibilitate: În depozitul extern

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This monograph is devoted to monoidal categories and their connections with 3-dimensional topologica...

Informații despre carte

Autor

Vladimir Turaev, Alexis Virelizier

Limbă

engleză

Legare

Carte - Carte broșată

Publicat

2018

Pagini

523

EAN

9783319842509

Enbook ID

20119167

Editura

Birkhauser Verlag AG

Greutate

813

Dimensiuni

155 x 235 x 29

Descriere completă

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.

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Monoidal Categories and Topological Field Theory

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