Functorial Knot Theory: Categories of Tangles, Coherence, Categorical Deformations and Topological Invariants
David N. Yetter, "Functorial Knot Theory: Categories of Tangles, Coherence, Categorical Deformations and Topological Invariants"
2001 | pages: 238 | ISBN: 9810244436 | PDF | 12,9 mb
2001 | pages: 238 | ISBN: 9810244436 | PDF | 12,9 mb
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 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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