Quantum Invariants : a Study of Knots, 3-Manifolds, and Their Sets.

Quantum Invariants : a Study of Knots, 3-Manifolds, and Their Sets.

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 grou...

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Bibliographic Details
Main Author: Ohtsuki, Tomotada
Format: eBook
Language:English
Published: Singapore : World Scientific Publishing Company, 2001.
Series:K & E series on knots and everything.
Subjects:
Quantum field theory.
Knot theory.
Three-manifolds (Topology)
Invariants.
Mathematical physics.
Invariants
Knot theory
Mathematical physics
Quantum field theory
Online Access:Click for online access
Table of 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.

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