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

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.

Product details

• Authors: David N Yetter, David N Yetter, David N. Yetter
• Publisher: Ingram Publishers Services
• Languages: English
• Product format: Hardback
• Released: 18.04.2001
• EAN: 9789810244439
• ISBN: 978-981-02-4443-9
• Series: Series on Knots & Everything; Series on Knots & Everything; Series on Knots and Everything; Knots and Everything
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Arithmetic, algebra; Algebra, MATHEMATICS / Geometry / Analytic, Number Theory, Algebraic Topology