Bibliographic Details
| Title: |
Deformations of standard locally homogeneous spaces. |
| Authors: |
KANNAKA, Kazuki1,2, KOBAYASHI, Toshiyuki3,4 |
| Source: |
Proceedings of the Japan Academy, Series A: Mathematical Sciences. Feb2026, Vol. 102 Issue 2, p7-12. 6p. |
| Subjects: |
Homogeneous spaces, Lie groups, Perturbation theory, Group actions (Mathematics), Discrete groups |
| Abstract: |
Let X 1/4 G=H be a homogeneous space, where G H are reductive Lie groups. We ask: in the setting where G=H is a standard quotient in the sense of Kassel-Kobayashi [9], 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 Γ\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. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
