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arXiv · 0909.2133

Surgery groups of the fundamental groups of hyperplane arrangement complements

S. Roushon
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Abstract

Using a recent result of Bartels and Lueck (arXiv:0901.0442) we deduce that the Farrell-Jones Fibered Isomorphism conjecture in L-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 the complex n-space.

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S. Roushon. 2009-09-11. Surgery groups of the fundamental groups of hyperplane arrangement complements. https://doi.org/10.1007/s00013-011-0243-4

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