FUNCTORIAL KNOT THEORY: CATEGORIES OF TANGLES, COHERENCE, CATEGORICAL DEFORMATIONS AND TOPOLOGICAL INVARIANTS: 26 (SERIES ON KNOTS AND EVERYTHING) - Hardcover

Yetter, David N

Hardcover

ISBN 10: 9810244436 ISBN 13: 9789810244439

Publisher: World Scientific Publishing Co Pte Ltd, 2001

Synopsis

Almost since the advent of skein-theoretic invariants of knots and links (the Jones, HOMFLY, and Kauffman polynomials), the important role of categories of tangles in the connection between low-dimensional topology and quantum-group theory has been recognized. The rich categorical structures naturally arising from the considerations of cobordisms have suggested functorial views of topological field theory.This book begins with a detailed exposition of the key ideas in the discovery of monoidal categories of tangles as central objects of study in low-dimensional topology. The focus then turns to the deformation theory of monoidal categories and the related deformation theory of monoidal functors, which is a proper generalization of Gerstenhaber's deformation theory of associative algebras. These serve as the building blocks for a deformation theory of braided monoidal categories which gives rise to sequences of Vassiliev invariants of framed links, and clarify their interrelations.

Edition details

• Publisher: World Scientific Publishing Co Pte Ltd
• Publication date: 2001
• Language: English
• ISBN 10: 9810244436
• ISBN 13: 9789810244439
• Binding: Hardcover
• Number of pages: 236