Kavli Affiliate: Toshiyuki Kobayashi
| First 5 Authors: Kazuki Kannaka, Kazuki Kannaka, , ,
| Summary:
Let $X=G/H$ be a homogeneous space of a Lie group $G$. When the isotropy
subgroup $H$ is non-compact, a discrete subgroup $Gamma$ may fail to act
properly discontinuously on $X$. In this article, we address the following
question: in the setting where $G$ and $H$ are reductive Lie groups and $Gamma
backslash X$ is a standard quotient, to what extent can one deform the
discrete subgroup $Gamma$ while preserving the proper discontinuity of the
action on $X$?
We provide several classification results, including conditions under which
local rigidity holds for compact standard quotients $Gammabackslash X$, when
a standard quotient can be deformed into a non-standard quotient, a
characterization of the largest Zariski-closure of discontinuous groups under
small deformations, and conditions under which Zariski-dense deformations
occur.
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