Algebra situs

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A branch of mathematics with roots in Jones' construction of his polynomial invariant of links, the Jones polynomial, and Drinfel'd's work on quantum groups (cf. also Quantum groups). It encompasses the theory of quantum invariants of knots and 3-manifolds, algebraic topology based on knots, $q$-deformations, quantum groups, and overlaps with algebraic geometry, non-commutative geometry and statistical mechanics.

The name algebra situs is motivated by terms coined by G. Leibniz: "geometria situs" and "analysis situs" .

For references, see Kauffman polynomial; Knot and link diagrams.

How to Cite This Entry:
Algebra situs. 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