Functorial knot theory : categories of tangles, coherence, categorical deformations, and topological invariants
著者
書誌事項
Functorial knot theory : categories of tangles, coherence, categorical deformations, and topological invariants
（Series on knots and everything, v. 26）
World Scientific, c2001
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注記
Includes bibliography (p. 219-224) and index
内容説明・目次
内容説明
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.
目次
- Part 1 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. Part 2 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. (Part contents).
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