A topological necessary condition for the existence of compact Clifford-Klein forms
Differential Geometry
2017-05-19 v2 Group Theory
Geometric Topology
Abstract
We provide a necessary condition for the existence of a compact Clifford-Klein form of a given homogeneous space of reductive type. The key to the proof is to combine a result of Kobayashi-Ono with an elementary fact that certain two different Clifford-Klein forms have the same cohomology ring. We give some examples, SL(p+q, R)/SO(p, q) (p, q: odd) for instance, of homogeneous spaces which do not admit compact Clifford-Klein forms.
Keywords
Cite
@article{arxiv.1310.7096,
title = {A topological necessary condition for the existence of compact Clifford-Klein forms},
author = {Yosuke Morita},
journal= {arXiv preprint arXiv:1310.7096},
year = {2017}
}
Comments
16 pages, revised following referee's comments, to appear in Journal of Differential Geometry