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Quantum Invariants : A Study Of Knots, 3-manifolds, And Their Sets - Tomotada Ohtsuki

Quantum Invariants

A Study Of Knots, 3-manifolds, And Their Sets

Hardcover

Published: 21st December 2001
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An extensive and self-contained presentation of quantum and related invariants of knots and 3-manifolds. Polynomial invariants of knots, such as the Jones and Alexander polynomials, are constructed as quantum invariants, in other words, invariants derived from representations of quantum groups and from the monodromy of solutions to the Knizhnik-Zamolodchikov equation. With the introduction of the Kontsevich invariant and the theory of Vassiliev invariants, the quantum invariants become well-organized. Quantum and perturbative invariants, the LMO invariant, and finite type invariants of 3-manifolds are discussed. The Chern-Simons field theory and the Wess-Zumino-Witten model are described as the physical background of the invariants.

Prefacep. v
Knots and polynomial invariantsp. 1
Braids and representations of the braid groupsp. 23
Operator invariants of tangles via sliced diagramsp. 41
Ribbon Hopf algebras and invariants of linksp. 63
Monodromy representations of the braid groups derived from the Knizhnik-Zamolodchikov equationp. 99
The Kontsevich invariantp. 133
Vassiliev invariantsp. 175
Quantum invariants of 3-manifoldsp. 211
Perturbative invariants of knots and 3-manifoldsp. 247
The LMO invariantp. 269
Finite type invariants of integral homology 3-spheresp. 305
The quantum group U[subscript q](sl[subscript 2])p. 333
The quantum sl[subscript 3] invariant via a linear skeinp. 349
Braid representations for the Alexander polynomialp. 357
Associatorsp. 365
Claspersp. 375
Physical backgroundp. 405
Computations for the perturbative invariantp. 437
The quantum sl[subscript 2] invariant and the Kauffman bracketp. 457
Bibliographyp. 463
Notationp. 483
Indexp. 485
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9789810246754
ISBN-10: 9810246757
Series: Series on Knots & Everything
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 508
Published: 21st December 2001
Publisher: World Scientific Publishing Co Pte Ltd
Country of Publication: SG
Dimensions (cm): 24.54 x 18.09  x 3.1
Weight (kg): 1.01