A rigidity Theorem and a Stability Theorem for two-step nilpotent Lie groups
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概要
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Let G be a Lie group and H a connected Lie subgroup of G. Given any discontinuous subgroup Γ for the homogeneous space X = G/H and any deformation of Γ, the deformed discrete subgroup may fail to be discontinuous for X. To understand this phenomenon in the case when G is a two-step nilpotent Lie group, we provide a stratification of the deformation space of the action of Γ on X, which depends upon the dimensions of G-adjoint orbits. As a direct consequence, a rigidity Theorem is given and a certain sufficient condition for the stability property is derived. We also discuss the Hausdorff property of the associated deformation space.
- Graduate School of Mathematical Sciences, The University of Tokyoの論文
- 2012-10-22
Graduate School of Mathematical Sciences, The University of Tokyo | 論文
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