Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A cohomological obstruction to the existence of compact Clifford-Klein
  forms   In this paper, we continue the study of the existence problem of compact
Clifford-Klein forms from a cohomological point of view, which was initiated by
Kobayashi-Ono and extended by Benoist-Labourie and the author. We give an
obstruction to the existence of compact Clifford-Klein forms by relating a
natural homomorphism from relative Lie algebra cohomology to de Rham cohomology
with an upper-bound estimate for cohomological dimensions of discontinuous
groups. From this obstruction, we derive some examples, e.g.
$\mathrm{SO}_0(p+r, q)/(\mathrm{SO}_0(p,q) \times \mathrm{SO}(r))$ $(p,q,r \geq
1, \ q:\text{odd})$ and $\mathrm{SL}(p+q, \mathbb{C})/\mathrm{SU}(p,q)$ $(p,q
\geq 1)$, of a homogeneous space that does not admit a compact Clifford-Klein
form. To construct these examples, we apply H. Cartan's theorem on relative Lie
algebra cohomology of reductive pairs and the theory of $\epsilon$-families of
semisimple symmetric pairs.

32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th