Abstract: In this article we show that the Whitehead group of any subgroup of the full Artin braid group vanish. In general we prove the same vanishing result for any torsion free subgroup of any finite extension of a strongly poly-free group. This result is a generalization of previous results of Bass-Heller-Swan (for free abelian groups) and Farrell-Hsiang (for finite extension of free abelian groups). In this paper we also answer in positive the conjecture posed in the paper "Algebraic K-theory of pure braid groups", which says that the Whitehead group of the fundamental group of any fiber-type hyperplane arrangement complement in the complex n-space vanish. (Recently Dan Cohen also proved this conjecture independently.) In fact in this paper we check that the Isomorphism Conjecture of Farrell-Jones is true for braid groups.
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