Overview

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.

Full Product Details

Author:   Tomotada Ohtsuki (Kyoto Univ, Japan)
Publisher:   World Scientific Publishing Co Pte Ltd
Imprint:   World Scientific Publishing Co Pte Ltd
Volume:   29
Dimensions:   Width: 18.10cm , Height: 3.10cm , Length: 23.00cm
Weight:   1.012kg
ISBN:  

9789810246754

ISBN 10:   9810246757
Pages:   508
Publication Date:   21 December 2001
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Out of stock  
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Table of Contents

Knots and polynomial invariants; braids and representations of the braid groups; operator invariants of tangles via sliced diagrams; Ribbon Hopf algebras and invariants of links; monodromy representations of the braid groups derived from the Knizhnik-Zamolodchikov equation; the Kontsevich invariant; Vassiliev invariants; quantum invariants of 3-manifolds; perturbative invariants of knots and 3-manifolds; the LMO invariant; finite type invariants of integral homology 3-spheres.

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