Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Proper actions of lattices on contractible manifolds   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.

30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom