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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 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 turn

Knot theory. --- Categories (Mathematics) --- Functor theory. --- Functorial representation --- Algebra, Homological --- Functional analysis --- Transformations (Mathematics) --- Category theory (Mathematics) --- Algebra, Universal --- Group theory --- Logic, Symbolic and mathematical --- Topology --- Functor theory --- Knots (Topology) --- Low-dimensional topology

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Mathematics