Quantum Invariants of Knots and 3-Manifolds /

Quantum Invariants of Knots and 3-Manifolds / / Vladimir G. Turaev.

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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 su...

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Bibliographic Details
Superior document:Title is part of eBook package: De Gruyter DGBA Mathematics - 1990 - 1999
VerfasserIn:
Turaev, Vladimir G.,
Place / Publishing House:Berlin ;, Boston : : De Gruyter, , [2020]
©1994
Year of Publication:2020
Edition:Reprint 2020
Language:English
Series:De Gruyter Studies in Mathematics , 18
Online Access:
Physical Description:1 online resource (588 p.) :; Num. figs.
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Table of Contents:
  • Frontmatter
  • Contents
  • Introduction
  • Part I. Towards Topological Field Theory
  • Chapter I. Invariants of graphs in Euclidean 3-space
  • Chapter II. Invariants of closed 3-manifolds
  • Chapter III. Foundations of topological quantum field theory
  • Chapter IV. Three-dimensional topological quantum field theory
  • Chapter V. Two-dimensional modular functors
  • Part II. The Shadow World
  • Chapter VI. 6j-symbols
  • Chapter VII. Simplicial state sums on 3-manifolds
  • Chapter VIII. Generalities on shadows
  • Chapter IX. Shadows of manifolds
  • Chapter X. State sums on shadows
  • Part III. Towards Modular Categories
  • Chapter XI. An algebraic construction of modular categories
  • Chapter XII. A geometric construction of modular categories
  • Appendix I. Dimension and trace re-examined
  • Appendix II. Vertex models on link diagrams
  • Appendix III. Gluing re-examined
  • Appendix IV. The signature of closed 4-manifolds from a state sum
  • Problems
  • References
  • Subject index

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