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Quantum Invariants of Knots and 3-Manifolds by Vladimir G. Turaev (Hardcover, 2016)

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This subject was inspired by the discovery of the Jones polynomial of knots and the Witten-Chern-Simons field theory. In Part II the technique of 6j-symbols is used to define state sum invariants of 3-manifolds.

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Due to the strong appeal and wide use of this monograph, it is now available in its third 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. Contents: Invariants of graphs in Euclidean 3-space and of closed 3-manifolds Foundations of topological quantum field theory Three-dimensional topological quantum field theory Two-dimensional modular functors 6j-symbols Simplicial state sums on 3-manifolds Shadows of manifolds and state sums on shadows Constructions of modular categories

Product Identifiers

Publisher
De Gruyter
ISBN-13
9783110442663
eBay Product ID (ePID)
224458057

Product Key Features

Author
Vladimir G. Turaev
Publication Name
Quantum Invariants of Knots and 3-Manifolds
Format
Hardcover
Language
English
Subject
Mathematics
Publication Year
2016
Type
Textbook
Number of Pages
608 Pages

Dimensions

Item Height
240mm
Item Width
170mm
Item Weight
1133g

Additional Product Features

Title_Author
Vladimir G. Turaev
Series Title
De Gruyter Studies in Mathematics
Country/Region of Manufacture
Germany

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Picture 1 of 1

Quantum Invariants of Knots and 3-Manifolds by Vladimir G. Turaev (Hardcover, 2016)

About this product

Product Information

Product Identifiers

Product Key Features

Dimensions

Additional Product Features

Best Selling in Adult Learning & University

A guide to the Project Management Body of Knowledge (PMBOK guide) and the Standard for project management by Project Management Institute (Paperback, 2021)

The Weed Forager's Handbook: A Guide to Edible and Medicinal Weeds in Australia by Adam Grubb, Annie Raser-Rowland (2012, Paperback)

Polyvagal Exercises for Safety and Connection: 50 Client-Centered Practices by Deb Dana (Paperback, 2020)

Save on Adult Learning & University

Ford Falcon EF, EL/Fairlane NF, NL/LTD DF, DL 1994-1998 Haynes Workshop Manual

Netter Atlas of Human Anatomy: Classic Regional Approach

Michael Price Nick Vandome Windows 11 for Seniors in easy steps (Paperback)

Dr. Robert Melillo Disconnected Kids - Revised and Updated (Paperback)

The Demon-Haunted World: Science as a Candle in the Dark by Carl Sagan (English)

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