Algebraic topology based on knots

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A branch of mathematics on the border of topology (cf. also Topology, general) and algebra, in which one analyzes properties of manifolds by considering links (submanifolds) in a manifold and their algebraic structure (cf. also Manifold). The main object of the discipline is the notion of skein module, i.e., the quotient of a free module over ambient isotopy classes of links in a manifold by properly chosen local ((skein)) relations.

For references, see Kauffman polynomial.

How to Cite This Entry:
Algebraic topology based on knots. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by J. Przytycki (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article