Deformations of Standard Locally Homogeneous Spaces

Kavli Affiliate: Toshiyuki Kobayashi

| First 5 Authors: Kazuki Kannaka, Kazuki Kannaka, , ,

| Summary:

Let $X=G/H$ be a homogeneous space, where $G supset H$ are reductive Lie
groups. We ask: in the setting where $Gamma backslash G/H$ is a standard
quotient, to what extent can the discrete subgroup $Gamma$ be deformed while
preserving the proper discontinuity of the $Gamma$-action on $X$?
We provide several classification results, including: conditions under which
local rigidity holds for compact standard quotients $Gammabackslash X$;
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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