Quantum Invariants of Knots and 3-Manifolds 2024 pdf epub mobi 電子書 下載


Quantum Invariants of Knots and 3-Manifolds

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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.

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發表於2024-12-23

Quantum Invariants of Knots and 3-Manifolds 2024 pdf epub mobi 電子書 下載

Quantum Invariants of Knots and 3-Manifolds 2024 pdf epub mobi 電子書 下載

Quantum Invariants of Knots and 3-Manifolds 2024 pdf epub mobi 電子書 下載



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出版者:Walter de Gruyter
作者:V. G. Turaev
出品人:
頁數:592
譯者:
出版時間:2010-04
價格:GBP 129.95
裝幀:Hardcover
isbn號碼:9783110221831
叢書系列:De Gruyter Studies in Mathematics

圖書標籤: 數學  Knots  3-Manifolds  量子拓撲  topology  張量範疇  凝聚態理論  TQFT   


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