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arXiv · 1310.7096

A topological necessary condition for the existence of compact Clifford-Klein forms

Yosuke Morita
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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.

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Yosuke Morita. 2013-10-26. A topological necessary condition for the existence of compact Clifford-Klein forms. https://doi.org/10.4310/jdg%2F1432842364

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