Monoidal Categories and Topological Field Theory 在线电子书 pdf 下载 txt下载 epub 下载 mobi 下载 2024

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Vladimir Turaev 作者

Birkhäuser

译者

2017 出版日期

523 页数

USD 127.09 价格

Hardcover

丛书系列

9783319498331 图书编码

Monoidal Categories and Topological Field Theory 在线电子书图书标签: 数学物理张量范畴凝聚态理论 topology TQFT

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Monoidal Categories and Topological Field Theory 在线电子书 epub 下载 mobi 下载 pdf 下载 txt 下载 2024

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Monoidal Categories and Topological Field Theory 在线电子书 pdf 下载 txt下载 epub 下载 mobi 在线电子书下载

Monoidal Categories and Topological Field Theory 在线电子书图书描述

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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