Quantum Invariants of Knots and 3 Manifolds by Vladimir G Turaev 9783110434569 3110434563

Quantum Invariants of Knots and 3 Manifolds Vladimir G Turaev – Ebook PDF Instant Download/Delivery ISBN(s): 9783110434569, 3110434563

Product details:

• ISBN 10: 3110434563
• ISBN 13: 9783110434569
• Author: Vladimir G Turaev 

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-manifolds Foundations of topological quantum field theory Three-dimensional topological quantum field theory Two-dimensional modular functors 6j-symbols Simplicial state sums on 3-manifolds Shadows of manifolds and state sums on shadows Constructions of modular categories

Table contents:

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

People also search:

quantum invariants of knots and 3-manifolds pdf

quantum invariants a study of knots 3-manifolds and their sets

knots and quantum theory

quantum edge 3 dimensions

what is rotational quantum number