Deformations of standard locally homogeneous spaces.
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| 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] |
| Copyright of Proceedings of the Japan Academy, Series A: Mathematical Sciences is the property of Japan Academy and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Links: – Type: pdflink Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 191566394 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Deformations of standard locally homogeneous spaces. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22KANNAKA%2C+Kazuki%22">KANNAKA, Kazuki</searchLink><relatesTo>1,2</relatesTo><br /><searchLink fieldCode="AR" term="%22KOBAYASHI%2C+Toshiyuki%22">KOBAYASHI, Toshiyuki</searchLink><relatesTo>3,4</relatesTo> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Proceedings+of+the+Japan+Academy%2C+Series+A%3A+Mathematical+Sciences%22">Proceedings of the Japan Academy, Series A: Mathematical Sciences</searchLink>. Feb2026, Vol. 102 Issue 2, p7-12. 6p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Homogeneous+spaces%22">Homogeneous spaces</searchLink><br /><searchLink fieldCode="DE" term="%22Lie+groups%22">Lie groups</searchLink><br /><searchLink fieldCode="DE" term="%22Perturbation+theory%22">Perturbation theory</searchLink><br /><searchLink fieldCode="DE" term="%22Group+actions+%28Mathematics%29%22">Group actions (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Discrete+groups%22">Discrete groups</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: 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] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Proceedings of the Japan Academy, Series A: Mathematical Sciences is the property of Japan Academy and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.3792/pjaa.102.002 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 6 StartPage: 7 Subjects: – SubjectFull: Homogeneous spaces Type: general – SubjectFull: Lie groups Type: general – SubjectFull: Perturbation theory Type: general – SubjectFull: Group actions (Mathematics) Type: general – SubjectFull: Discrete groups Type: general Titles: – TitleFull: Deformations of standard locally homogeneous spaces. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: KANNAKA, Kazuki – PersonEntity: Name: NameFull: KOBAYASHI, Toshiyuki IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 02 Text: Feb2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 03862194 Numbering: – Type: volume Value: 102 – Type: issue Value: 2 Titles: – TitleFull: Proceedings of the Japan Academy, Series A: Mathematical Sciences Type: main |
| ResultId | 1 |
