In 1962, Fadell and Neuwirth showed that the configuration space of the
braid arrangement is aspherical. Having generalized this to many real
reflection groups, Brieskorn conjectured this for all finite Coxeter groups.
This in turn follows from Deligne’s seminal work from 1972, where he
showed that the complexification of every real simplicial arrangement is a
–arrangement.
We study the
–property
for a certain class of subarrangements of Weyl arrangements, the so-called arrangements of ideal
type
. These stem
from ideals
in the set of positive roots of a reduced root system. We show that the
–property holds for
all arrangements
if the underlying Weyl group is classical and that it extends to most of the
if the
underlying Weyl group is of exceptional type. Conjecturally this holds for all
. In general,
the
are neither simplicial nor is their complexification of fiber type.
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Institut für
Algebra, Zahlentheorie und Diskrete Mathematik
Fakultät für Mathematik und Physik
Gottfried Wilhelm Leibniz Universität Hannover
Hannover
Germany