Kavli Affiliate: Toshiyuki Kobayashi
| Summary:
Let $X=G/H$ be a homogeneous space, where $G supset H$ are reductive Lie groups. We ask: in the setting where $Γbackslash G/H$ is a standard quotient, to what extent can the discrete subgroup $Γ$ be deformed while preserving the proper discontinuity of the $Γ$-action on $X$?
We provide several classification results, including: conditions under which local rigidity holds for compact standard quotients $Γbackslash X$; criteria for when a standard quotient can be deformed into a nonstandard one; a characterization of the maximal Zariski-closure of discontinuous groups under small deformations; and conditions under which Zariski-dense deformations occur.
Proofs of the results stated in this paper are provided in detail in arXiv:2507.03476.
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