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Monoidal Categories and Topological Field Theory (in English)
Vladimir Turaev
(Author)
·
Alexis Virelizier
(Author)
·
Birkhauser
· Paperback
Monoidal Categories and Topological Field Theory (in English) - Turaev, Vladimir ; Virelizier, Alexis
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Synopsis "Monoidal Categories and Topological Field Theory (in English)"
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 tothe 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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All books in our catalog are Original.
The book is written in English.
The binding of this edition is Paperback.
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