Turaev Quantum Invariants of Knots and 3-Manifolds

2. revidierte ed
ISBN: 978-3-11-022184-8
Verlag: De Gruyter
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 18, 604 Seiten

Reihe: De Gruyter Studies in Mathematics

This monograph, now in its second revised edition, provides a systematic treatment of topological quantum field theories 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 subject, gives a rigorous and self-contained exposition of fundamental algebraic and topological concepts that emerged in this theory.

Zielgruppe

Researchers, Graduate Students of Mathematics; Academic Libraries

Autoren/Hrsg.

Turaev, Vladimir G.

Fachgebiete

• Mathematik | Informatik Mathematik Topologie Algebraische Topologie
• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
• Mathematik | Informatik Mathematik Algebra

Inhaltsverzeichnis

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
Backmatter

Über Autor(innen)

Turaev, Vladimir G.
Vladimir G. Turaev, Indiana University, Bloomington, USA