Grupo de tranças e espaços de configurações

Abstract

In this work, we study the Artin braid group, B(n), and the confguration spaces (ordered and unordered) of a path connected manifold of dimension ¸ 2. The fundamental group of confguration space (unordered) of IR2 is identifed with the Artin braid group. This identifcation is used to conclude that the confguration space of IR2 is an Eilenberg-MacLane space of type K(B(n), 1). Therefore, it can be proved that the braid group B(n) contains no nontrivial element of the finite order. We use this fact to prove a generalization of a 2−dimensional version of the Borsuk-Ulam theorem presented by Connett [3].