Affine Configurations and Pure Braids

We show that the fundamental group of ordered affine-equivalent configurations with at least five points in the real plane is isomorphic to the pure braid group in as many strands, modulo its centre. In the case of four points, this fundamental group is free with 11 generators. This work was carried out at the Instituto de Matemáticas, UNAM and partially funded by the Sistema Nacional de Investigadores and a doctoral fellowship from CONACyT México.