Quantum Invariants of Knots and 3-Manifolds

Name: Quantum Invariants of Knots and 3-Manifolds
Brand: de Gruyter
SKU: 9783110137040
Price: 19676.0 INR
Availability: InStock

by Vladimir G. Turaev

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ISBN13: 9783110137040
Binding: Hardcover
Subject: N/A
Publisher: de Gruyter
Publisher Imprint: de Gruyter
Publication Date: July 1, 1994
Pages: 598
Original Price: GBP 154.5
Language: English
Edition: Reprint 2020
Item Weight: 1148 grams
BISAC Subject(s): Algebra / Linear

About The Book

This monograph provides a systematic treatment of topological quantum field theories (TQFT's) in three dimensions, inspired by the discovery of the Jones polynomial of knots, the Witten-Chern-Simons field theory, and the theory of quantum groups. The author, one of the leading experts in the subject, gives a rigorous and self-contained exposition of new fundamental algebraic and topological concepts that emerged in this theory.

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

This book is accessible to graduate students in mathematics and physics with a knowledge of basic algebra and topology. It will be an indispensable source for everyone who wishes to enter the forefront of this rapidly growing and fascinating area at the borderline of mathematics and physics. Most of the results and techniques presented here appear in book form for the first time.

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