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arXiv · 1503.02186

Homogeneous space with non virtually abelian discontinuous groups but without any proper SL(2,R)-action

Takayuki Okuda
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Abstract

In the study of discontinuous groups for non-Riemannian homogeneous spaces, the idea of "continuous analogue" gives a powerful method (T. Kobayashi [Math. Ann. 1989]). For example, a semisimple symmetric space G/H admits a discontinuous group which is not virtually abelian if and only if G/H admits a proper SL(2,R)-action (T. Okuda [J. Differential Geom. 2013]). However, the action of discrete subgroups is not always approximated by that of connected groups. In this paper, we show that the theorem cannot be extended to general homogeneous spaces G/H of reductive type. We give a counterexample in the case G = SL(5,R).

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Takayuki Okuda. 2015-03-07. Homogeneous space with non virtually abelian discontinuous groups but without any proper SL(2,R)-action. https://arxiv.org/abs/1503.02186

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