Proper actions of lattices on contractible manifolds

Details Proper actions of lattices on contractible manifolds Proper actions of lattices on contractible manifolds

2000-11-28

arxiv.org/abs/math/0011238v1

Mathematics

Geometric Topology

32 pages

Scientific paper

Every lattice H 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 H 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 is not less than dim G/K.

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