Functorial Knot Theory: Categories Of Tangles, Coherence, Categorical Deformations And Topological Invariants

Categories of Tangles, Coherence, Categorical Deformations, and Topological Invariants

David N Yetter

• Publisher: World Scientific
• Year: 2001
• Print ISBN: 9789810244439, 9789810244439
• eBook ISBN: 9789812810465
• Topic: Mathematics
• Subtopic: Analytic Geometry
• Index: Mathematics

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.

Table of contents

• Contents
• Acknowledgements
• 1. Introduction
• I Knots and Categories
• II Deformations
• Bibliography
• Index