Quantum invariants : a study of knots, 3-manifolds, and their sets / Tomotada Ohtsuki.

Format:

Book

Author/Creator:

Ohtsuki, Tomotada.

Series:

K & E series on knots and everything ; v. 29.

K & E series on knots and everything ; 29

Language:

English

Subjects (All):

Quantum field theory.

Knot theory.

Three-manifolds (Topology).

Invariants.

Mathematical physics.

Physical Description:

1 online resource (508 p.)

Edition:

1st ed.

Place of Publication:

Singapore ; River Edge, NJ : World Scientific, c2002.

Language Note:

English

Summary:

This book provides 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, i.e. 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 o

Contents:

Contents ; Preface ; Chapter 1 Knots and polynomial invariants ; 1.1 Knots and their diagrams ; 1.2 The Jones polynomial ; 1.3 The Alexander polynomial ; Chapter 2 Braids and representations of the braid groups ; 2.1 Braids and braid groups

2.2 Representations of the braid groups via R matrices 2.3 Burau representation of the braid groups ; Chapter 3 Operator invariants of tangles via sliced diagrams ; 3.1 Tangles and their sliced diagrams ; 3.2 Operator invariants of unoriented tangles

3.3 Operator invariants of oriented tangles Chapter 4 Ribbon Hopf algebras and invariants of links ; 4.1 Ribbon Hopf algebras ; 4.2 Invariants of links in ribbon Hopf algebras ; 4.3 Operator invariants of tangles derived from ribbon Hopf algebras

4.4 The quantum group Uq(sl2) at a generic q 4.5 The quantum group Uc(sl2) at a root of unity C ; Chapter 5 Monodromy representations of the braid groups derived from the Knizhnik-Zamolodchikov equation ; 5.1 Representations of braid groups derived from the KZ equation

5.2 Computing monodromies of the KZ equation 5.3 Combinatorial reconstruction of the monodromy representations ; 5.4 Quasi-triangular quasi-bialgebra ; 5.5 Relation to braid representations derived from the quantum group ; Chapter 6 The Kontsevich invariant ; 6.1 Jacobi diagrams

6.2 The Kontsevich invariant derived from the formal KZ equation

Notes:

Description based upon print version of record.

Includes bibliographical references (p. 463-481) and index.

ISBN:

9786611956677

9781281956675

1281956678

9789812811172

9812811176

OCLC:

879023732