Abstract
Using a recent result of Bartels and Lück (The Borel conjecture for hyperbolic and CAT(0)-groups (preprint) \({{\tt arXiv:0901.0442v1}}\)) we deduce that the Farrell–Jones Fibered Isomorphism conjecture in \({L^{\langle -\infty \rangle}}\)-theory is true for any group which contains a finite index strongly poly-free normal subgroup, in particular, for the Artin full braid groups. As a consequence we explicitly compute the surgery groups of the Artin pure braid groups. This is obtained as a corollary to a computation of the surgery groups of a more general class of groups, namely for the fundamental group of the complement of any fiber-type hyperplane arrangement in \({{\mathbb C}^n}\).
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Roushon, S. Surgery groups of the fundamental groups of hyperplane arrangement complements. Arch. Math. 96, 491–500 (2011). https://doi.org/10.1007/s00013-011-0243-4
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DOI: https://doi.org/10.1007/s00013-011-0243-4