
School of Mathematics and Statistics
Eddy Godelle
University of Sydney
Buildings associated with ArtinTits groups of spherical type.
Friday 5th April, 121pm,
Carslaw 373.
Let V be a finite dimensional vector space over
R and let W be a finite subgroup of
GL(V) generated by reflections such that
$V^{W} = {0}$. We can associate to V a Euclidean
structure which is W invariant. Denote by M the set
of hyperplanes associated to the orthogonal reflections of W.
Consider V_{C}, the complexification of
V, and m_{C} the complexification of
m for m in M. Let
Y_{W} = V_C  \cup_{M\in M}M_{C}
and X_{W} = Y_{W}/W.
Deligne (Invent. 1972) proved that X_{W} is a
K(\pi,1)space and that
\Pi_{1}(X_{W}, x) is the ArtinTits group
associated to W for any x\in X_{W}. We will
describe the notion of "gallery" he introduced in its proof and
explain the main ideas of its proof.
