Difference between revisions of "Algebraic topology based on knots"
From Encyclopedia of Mathematics
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A branch of mathematics on the border of topology (cf. also [[Topology, general|Topology, general]]) and [[Algebra|algebra]], in which one analyzes properties of manifolds by considering links (submanifolds) in a manifold and their algebraic structure (cf. also [[Manifold|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. | A branch of mathematics on the border of topology (cf. also [[Topology, general|Topology, general]]) and [[Algebra|algebra]], in which one analyzes properties of manifolds by considering links (submanifolds) in a manifold and their algebraic structure (cf. also [[Manifold|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|Kauffman polynomial]]. | For references, see [[Kauffman polynomial|Kauffman polynomial]]. | ||
Latest revision as of 09:12, 4 May 2014
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
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