Surgery groups of the fundamental groups of hyperplane arrangement complements

Details Surgery groups of the fundamental groups of hyperplane arrangement complements Surgery groups of the fundamental groups of hyperplane arrangement complements

2009-09-11

arxiv.org/abs/0909.2133v2

Mathematics

K-Theory and Homology

11 pages, AMSLATEX file, revised following referee's comments and suggestions, to appear in Archiv der Mathematik

Scientific paper

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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