Every lattice Γ in a connected semi-simple Lie group
G acts properly discontinuously by isometries on the contractible manifold
G/
K (
K a maximal compact subgroup of
G). We prove that if Γ acts on a contractible manifold
W and if either¶1) the action is properly discontinuous, or¶2)
W is equipped with a complete Riemannian metric, the action is by isometries and with unbounded orbits,
G is simple with finite center and rank >1,¶then dim
W≥dim
G/
K.
Oblatum 19-I-2001 & 24-IV-2002¶Published online: 5 September 2002
RID="*"
ID="*"The authors gratefully acknowledge support from the National Science Foundation.