Difference between revisions of "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|Quantum groups]]). It encompasses the theory of quantum invariants of knots and | + | {{TEX|done}} |
| + | 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|Quantum groups]]). It encompasses the theory of quantum invariants of knots and 3-manifolds, [[Algebraic topology based on knots|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" . | The name algebra situs is motivated by terms coined by G. Leibniz: "geometria situs" and "analysis situs" . | ||
For references, see [[Kauffman polynomial|Kauffman polynomial]]; [[Knot and link diagrams|Knot and link diagrams]]. | For references, see [[Kauffman polynomial|Kauffman polynomial]]; [[Knot and link diagrams|Knot and link diagrams]]. | ||
Latest revision as of 06:33, 23 April 2012
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: http://encyclopediaofmath.org/index.php?title=Algebra_situs&oldid=18773
Algebra situs. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Algebra_situs&oldid=18773
This article was adapted from an original article by J. Przytycki (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article