Quantum Invariants of Knots and 3-Manifolds pdf epub mobi txt 电子书 下载 2024


Quantum Invariants of Knots and 3-Manifolds

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V. G. Turaev
Walter de Gruyter
2010-04
592
GBP 129.95
Hardcover
De Gruyter Studies in Mathematics
9783110221831

图书标签: 数学  Knots  3-Manifolds  量子拓扑  topology  张量范畴  凝聚态理论  TQFT   


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发表于2024-12-25

Quantum Invariants of Knots and 3-Manifolds epub 下载 mobi 下载 pdf 下载 txt 电子书 下载 2024

Quantum Invariants of Knots and 3-Manifolds epub 下载 mobi 下载 pdf 下载 txt 电子书 下载 2024

Quantum Invariants of Knots and 3-Manifolds pdf epub mobi txt 电子书 下载 2024



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Due to the strong appeal and wide use of this monograph, it is now available in its second revised edition. The monograph gives a systematic treatment of 3-dimensional topological quantum field theories (TQFTs) based on the work of the author with N. Reshetikhin and O. Viro. This subject was inspired by the discovery of the Jones polynomial of knots and the Witten-Chern-Simons field theory. On the algebraic side, the study of 3-dimensional TQFTs has been influenced by the theory of braided categories and the theory of quantum groups.

The book is divided into three parts. Part I presents a construction of 3-dimensional TQFTs and 2-dimensional modular functors from so-called modular categories. This gives a vast class of knot invariants and 3-manifold invariants as well as a class of linear representations of the mapping class groups of surfaces. In Part II the technique of 6j-symbols is used to define state sum invariants of 3-manifolds. Their relation to the TQFTs constructed in Part I is established via the theory of shadows. Part III provides constructions of modular categories, based on quantum groups and skein modules of tangles in the 3-space.

This fundamental contribution to topological quantum field theory is accessible to graduate students in mathematics and physics with knowledge of basic algebra and topology. It is an indispensable source for everyone who wishes to enter the forefront of this fascinating area at the borderline of mathematics and physics.

Quantum Invariants of Knots and 3-Manifolds 下载 mobi epub pdf txt 电子书

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