Grupo de tranças e espaços de configurações
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Data
2007-06-27Autor
Maríngolo, Fernanda Palhares
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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].