On the geometry of stable discontinuous subgroups acting on threadlike homogeneous spaces |
| |
Authors: | A Baklouti F Khlif H Koubaa |
| |
Institution: | 1. Department of Mathematics, Sfax University, Sfax, Tunisia
|
| |
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 ?(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 ?(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 ?(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. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|