ACTUELLEMENT ÉPUISÉ

Series on Knots and Everything: Functorial Knot Theory : Categories of Tangles, Coherence, Categorical Deformations and Topological Invariants by David N. Yetter (2000, Hardcover)

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.

Author
David N. Yetter
Publication Name
Functorial Knot Theory : Categories of Tangles, Coherence, Categorical Deformations and Topological Invariants
Format
Hardcover
Language
English
Subject
Group Theory, Geometry / Analytic, Functional Analysis, Topology
Series
Series on Knots and Everything
Publication Year
2000
Type
Textbook
Subject Area
Mathematics
Number of Pages
230 Pages

Explorer par catégorie