Functionary knot theory

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

David N. Yetter

230 pages, parution le 01/06/2001

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Résumé

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.

Contents

Knots and Categories: Monoidal Categories, Functors and Natural Transformations
A Digression on Algebras
Knot Polynomials
Smooth Tangles and PL Tangles
A Little Enriched Category Theory
Deformations: Deformation Complexes of Semigroupal Categories and Functors
First Order Deformations
Units
Extrinsic Deformations of Monoidal Categories
Categorical Deformations as Proper Generalizations of Classical Notions
and other papers

Caractéristiques techniques

	PAPIER
Éditeur(s)	World Scientific
Auteur(s)	David N. Yetter
Parution	01/06/2001
Nb. de pages	230
Format	15,5 x 22,3
Couverture	Relié
Poids	468g
Intérieur	Noir et Blanc
EAN13	9789810244439