braidgroep
The braid group B_n, in Dutch mathematics called the braidgroep, consists of braids on n strands in three-dimensional space, with the group operation given by concatenation. An element is an equivalence class of braids with fixed endpoints, modulo ambient isotopy that preserves the endpoints.
A standard presentation uses generators sigma_1, ..., sigma_{n-1}, with relations sigma_i sigma_j = sigma_j sigma_i for |i - j|
Braid groups have several important realizations and connections. They are the mapping class group of the n-punctured
Applications and theory: braid groups underpin much of knot theory, since every link is the closure of
For n ≥ 3, B_n is infinite and non-abelian; its center is trivial, while B_2 is isomorphic to