Functorial Knot Theory: Categories of Tangles, Coherence, Categorical Deformations, and Topological Invariants. Series on Knots and Everything, Volume 26 |
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Author:
| Yetter, David N. |
Series title: | Series on Knots and Everything Ser. |
ISBN: | 978-1-281-95616-3 |
Publication Date: | Jan 2001 |
Publisher: | World Scientific Publishing Co Pte Ltd
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Book Format: | Ebook |
List Price: | USD $100.00 |
Book Description:
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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 structure 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...
More DescriptionAlmost 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 structure 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.