NDLI: On the geometry of stable discontinuous subgroups acting on threadlike homogeneous spaces

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On the geometry of stable discontinuous subgroups acting on threadlike homogeneous spaces

Content Provider	Springer Nature Link
Author	Baklouti, A. Khlif, F. Koubaa, H.
Copyright Year	2011
Abstract	Following the notion of stability introduced by T. Kobayashi and S. Nasrin in [14], we show in the context of a threadlike Lie group G that any non-Abelian discrete subgroup is stable. One consequence is that any resulting deformation space ℐ(Γ,G,H) is a Hausdorff space, where Γ acts on the threadlike homogeneous space G/H as a discontinuous subgroup. Whenever k = rank(Γ) > 3, this space is also shown to be endowed with a smooth manifold structure. But if k = 3, then ℐ(Γ,G,H) admits a smooth manifold structure as its open dense subset. These phenomena are strongly linked to the features of adjoint orbits of the basis group G on the parameter space ℛ(Γ,G,H) (which is semi-algebraic in this case) and specifically to their dimensions, as it will be seen throughout the paper. This also allows to provide a proof of the Local Rigidity Conjecture in this setup.
Starting Page	761
Ending Page	776
Page Count	16
File Format	PDF
ISSN	00014346
Journal	Mathematical Notes
Volume Number	89
Issue Number	5-6
e-ISSN	15738876
Language	English
Publisher	SP MAIK Nauka/Interperiodica
Publisher Date	2011-06-29
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	threadlike Lie group stable subgroup discrete subgroup deformation space rigidity Lie algebra discontinuous action smooth manifold Hausdorff space Mathematics
Content Type	Text
Resource Type	Article

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