# Algebraic topology based on knots

From Encyclopedia of Mathematics

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: http://encyclopediaofmath.org/index.php?title=Algebraic_topology_based_on_knots&oldid=32140

This article was adapted from an original article by J. Przytycki (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article