Group theory MOC

Braid group

Let be a topological space, and denote the space of subsets of of cardinality .¹ The braid group on strands in is the fundamental group

In the special case is the Euclidean plane, we have the Artin braid group.

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Footnotes

1. The natural topology on is that of the orbit space (quotient topology) of [[Symmetric group|]] acting on the subspace topology of the product space where consists of points with at least two components the same. ↩