Surgery groups of the fundamental groups of hyperplane arrangement complements
K-Theory and Homology
2012-05-21 v2 Geometric Topology
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.
Keywords
Cite
@article{arxiv.0909.2133,
title = {Surgery groups of the fundamental groups of hyperplane arrangement complements},
author = {S. Roushon},
journal= {arXiv preprint arXiv:0909.2133},
year = {2012}
}
Comments
11 pages, AMSLATEX file, revised following referee's comments and suggestions, to appear in Archiv der Mathematik