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An Entity of Type : yago:WikicatDiagramAlgebras, within Data Space : dbpedia.org associated with source document(s)

Type: Thingyago:WikicatBraidGroupsyago:Abstraction100002137yago:Algebra106012726yago:Cognition100023271yago:Content105809192yago:Discipline105996646yago:Group100031264yago:KnowledgeDomain105999266yago:Mathematics106000644yago:PsychologicalFeature100023100yago:PureMathematics106003682Bandyago:Science105999797yago:WikicatDiagramAlgebras New Facet based on Instances of this Class

In mathematics, the braid group on n strands (denoted ), also known as the Artin braid group, is the group whose elements are equivalence classes of n-braids (e.g. under ambient isotopy), and whose group operation is composition of braids (see ). Example applications of braid groups include knot theory, where any knot may be represented as the closure of certain braids (a result known as Alexander's theorem); in mathematical physics where Artin's canonical presentation of the braid group corresponds to the Yang–Baxter equation (see ); and in monodromy invariants of algebraic geometry.