Braid group

B3 is the universal central extension of the modular group.

In mathematics: the braid group on $n$ strands, denoted by $B n$ , is a group that generalizes the symmetric group $S n$ . Here, $n$ 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 $n > 1$ , then $B n$ is an infinite group.

单词	Braid group
释义	Braid group 英语百科 Braid group In mathematics: the braid group on $n$ strands, denoted by $B n$ , is a group that generalizes the symmetric group $S n$ . Here, $n$ 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 $n > 1$ , then $B n$ is an infinite group.
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