On representations and K-theory of the braid groups

@article{Adem2001OnRA,
  title={On representations and K-theory of the braid groups},
  author={Alejandro Adem and Daniel C. Cohen and Frederick R. Cohen},
  journal={Mathematische Annalen},
  year={2001},
  volume={326},
  pages={515-542}
}
Abstract. Let Γ be the fundamental group of the complement of a K(Γ, 1) hyperplane arrangement (such as Artin's pure braid group) or more generally a homologically toroidal group as defined below. The triviality of bundles arising from orthogonal representations of Γ is characterized completely as follows. An orthogonal representation gives rise to a trivial bundle if and only if the representation factors through the spinor groups. Furthermore, the subgroup of elements in the complex K-theory… 

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