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braid group

n. (context group theory English) a (l/en: group) whose elements represent ways to (l/en: weave) some number of (l/en string strings) into (l/en braid braids)

Braid group

In mathematics: the braid group on strands, denoted by , is a certain group having the symmetric group as a quotient group. Here, is a natural number, representing a number of points to be permuted as strands. The presented monoid of elements from the symmetric group defines a permutation of those points from the initial to final configuration. An element of the braid group describes an initial and final configuration of these points, as well as how the stepwise configurations are composed by continuously moving the initial points to their final configurations. If , then is an infinite group.

Braid groups find applications in knot theory, since any knot may be represented as the closure of certain braids.