Autor: Vladimir G. Turaev
ISBN-13: 9783110442663
Einband: Buch
Seiten: 596
Format: 244x174x38 mm
Sprache: Englisch

Quantum Invariants of Knots and 3-Manifolds

18, De Gruyter Studies in Mathematics
In den Warenkorb
149,95 €
Due to the strong appeal and wide use of this monograph, it is now available in its third revised edition. The monograph gives a systematic treatment of 3-dimensional topological quantum field theories (TQFTs) based on the work of the author with N. Reshetikhin and O. Viro. This subject was inspired by the discovery of the Jones polynomial of knots and the Witten-Chern-Simons field theory. On the algebraic side, the study of 3-dimensional TQFTs has been influenced by the theory of braided categories and the theory of quantum groups.The book is divided into three parts. Part I presents a construction of 3-dimensional TQFTs and 2-dimensional modular functors from so-called modular categories. This gives a vast class of knot invariants and 3-manifold invariants as well as a class of linear representations of the mapping class groups of surfaces. In Part II the technique of 6j-symbols is used to define state sum invariants of 3-manifolds. Their relation to the TQFTs constructed in Part I is established via the theory of shadows. Part III provides constructions of modular categories, based on quantum groups and skein modules of tangles in the 3-space.This fundamental contribution to topological quantum field theory is accessible to graduate students in mathematics and physics with knowledge of basic algebra and topology. It is an indispensable source for everyone who wishes to enter the forefront of this fascinating area at the borderline of mathematics and physics. Contents:Invariants of graphs in Euclidean 3-space and of closed 3-manifoldsFoundations of topological quantum field theoryThree-dimensional topological quantum field theoryTwo-dimensional modular functors6j-symbolsSimplicial state sums on 3-manifoldsShadows of manifolds and state sums on shadowsConstructions of modular categories
Autor: Vladimir G. Turaev
Vladimir G. Turaev, Indiana University, Bloomington, USA.

Zu diesem Artikel ist noch keine Rezension vorhanden.
Helfen sie anderen Besuchern und verfassen Sie selbst eine Rezension.

 

Rezensionen

Autor: Vladimir G. Turaev
ISBN-13:: 9783110442663
ISBN: 3110442663
Erscheinungsjahr: 11.07.2016
Verlag: Gruyter, Walter de GmbH
Gewicht: 1138g
Seiten: 596
Sprache: Englisch
Auflage 16003, 3rd corr. ed
Sonstiges: Buch, 244x174x38 mm