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Functorial Knot Theory

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

By: David N. Yetter

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Functorial Knot Theory

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

By: David N. Yetter

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.

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Page Count

238

Publisher

World Scientific

Published Date

ISBN 10

9810244436

ISBN 13

9789810244439

Diagrammatic Morphisms and Applications

AMS Special Session on Diagrammatic Morphisms in Algebra, Category Theory, and Topology, October 21-22, 2000, San Francisco State University, San Francisco, California

By: David E. Radford,David N. Yetter

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Diagrammatic Morphisms and Applications

AMS Special Session on Diagrammatic Morphisms in Algebra, Category Theory, and Topology, October 21-22, 2000, San Francisco State University, San Francisco, California

By: David E. Radford,David N. Yetter

The technique of diagrammatic morphisms is an important ingredient in comprehending and visualizing certain types of categories with structure. It was widely used in this capacity in many areas of algebra, low-dimensional topology and physics. It was also applied to problems in classical and quantum information processing and logic. This volume contains articles based on talks at the Special Session, ``Diagrammatic Morphisms in Algebra, Category Theory, and Topology'', at the AMS Sectional Meeting in San Francisco. The articles describe recent achievements in several aspects of diagrammatic morphisms and their applications. Some of them contain detailed expositions on various diagrammatic techniques. The introductory article by D. Yetter is a thorough account of the subject in a historical perspective.

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Page Count

232

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821827944

ISBN 13

9780821827949