Wow! eBook
Functorial Knot Theory : Categories of Tangles, Coherence, Categorical Deformations and Topological Invariants
Author:David N Yetter (Author)
Publisher: World Scientific Publishing Company
Publication date: 2001-04-18
Edition: Illustrated
Language: English
Print length: 236 pages
ISBN-10: 9810244436
ISBN-13: 9789810244439
Book Description
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.
