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July 2015 A topological necessary condition for the existence of compace Clifford-Klein forms
Yosuke Morita
J. Differential Geom. 100(3): 533-545 (July 2015). DOI: 10.4310/jdg/1432842364

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 and Ono with the observation that a fiber bundle with contractible fiber induces an isomorphism between the cohomology rings of the total space and the base space. We give some examples: $SL(p + q,\mathbb{R})/SO(p, q)(p, q : \mathrm{odd})$, for instance—of homogeneous spaces that do not admit compact Clifford–Klein forms.

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Yosuke Morita. "A topological necessary condition for the existence of compace Clifford-Klein forms." J. Differential Geom. 100 (3) 533 - 545, July 2015. https://doi.org/10.4310/jdg/1432842364

Information

Published: July 2015
First available in Project Euclid: 28 May 2015

zbMATH: 1323.53056
MathSciNet: MR3352798
Digital Object Identifier: 10.4310/jdg/1432842364

Rights: Copyright © 2015 Lehigh University

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Vol.100 • No. 3 • July 2015
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