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- Title
Surgery groups of the fundamental groups of hyperplane arrangement complements.
- Authors
ROUSHON, S.
- 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 $${{\mathbb C}^n}$$.
- Subjects
SET theory; BOREL sets; ISOMORPHISM (Mathematics); HYPERSETS; ALGEBRA
- Publication
Archiv der Mathematik, 2011, Vol 96, Issue 5, p491
- ISSN
0003-889X
- Publication type
Article
- DOI
10.1007/s00013-011-0243-4