Monoidal Categories and Topological Field Theory 在線電子書 pdf 下載 txt下載 epub 下載 mobi 下載 2024

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Vladimir Turaev 作者

Birkhäuser

譯者

2017 出版日期

523 頁數

USD 127.09 價格

Hardcover

叢書系列

9783319498331 圖書編碼

Monoidal Categories and Topological Field Theory 在線電子書圖書標籤: 數學物理張量範疇凝聚態理論 topology TQFT

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發表於2024-11-16

Monoidal Categories and Topological Field Theory 在線電子書 epub 下載 mobi 下載 pdf 下載 txt 下載 2024

Monoidal Categories and Topological Field Theory 在線電子書 epub 下載 pdf 下載 mobi 下載 txt 下載 2024

Monoidal Categories and Topological Field Theory 在線電子書 pdf 下載 txt下載 epub 下載 mobi 下載 2024

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Monoidal Categories and Topological Field Theory 在線電子書 pdf 下載 txt下載 epub 下載 mobi 在線電子書下載

Monoidal Categories and Topological Field Theory 在線電子書圖書描述

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 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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