| 书目名称 | Monoidal Categories and Topological Field Theory | | 编辑 | Vladimir Turaev,Alexis Virelizier | | 视频video | | | 概述 | Offers a detailed exposition accessible to students.Provides numerous figures.Winner of the 2016 Ferran Sunyer i Balaguer Prize | | 丛书名称 | Progress in Mathematics | | 图书封面 |  | | 描述 | .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 | | 出版日期 | Book 2017 | | 关键词 | monoidal categories; Hopf algebras; Hopf monads; 3-manifold invariants; topological quantum field theory | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-319-49834-8 | | isbn_softcover | 978-3-319-84250-9 | | isbn_ebook | 978-3-319-49834-8Series ISSN 0743-1643 Series E-ISSN 2296-505X | | issn_series | 0743-1643 | | copyright | Springer International Publishing AG 2017 |
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发表于 2025-3-21 16:05:07
