Local spectral gap in the group of Euclidean isometries
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | BOUTONNET, Rémi | |
| hal.structure.identifier | Mathematics Department; University of California San Diego | |
| dc.contributor.author | IOANA, Adrian | |
| dc.date.accessioned | 2024-04-04T03:04:49Z | |
| dc.date.available | 2024-04-04T03:04:49Z | |
| dc.date.issued | 2018-03-12 | |
| dc.identifier.issn | 1073-7928 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/193187 | |
| dc.description.abstractEn | We provide new examples of translation actions on locally compact groups with the "local spectral gap property" introduced in [BISG15]. This property has applications to strong ergodicity, the Banach-Ruziewicz problem, orbit equivalence rigidity, and equidecomposable sets. The main group of study here is the group Isom(R d) of orientation-preserving isometries of the euclidean space R d , for d ≥ 3. We prove that the translation action of a countable dense subgroup Γ on Isom(R d) has local spectral gap, whenever the translation action of the rotation projection of Γ on SO(d) has spectral gap. Our proof relies on the amenability of Isom(R d) and on work of Lindenstrauss and Varjú, [LV14]. | |
| dc.language.iso | en | |
| dc.publisher | Oxford University Press (OUP) | |
| dc.title.en | Local spectral gap in the group of Euclidean isometries | |
| dc.type | Article de revue | |
| dc.subject.hal | Mathématiques [math]/Théorie des groupes [math.GR] | |
| dc.subject.hal | Mathématiques [math]/Systèmes dynamiques [math.DS] | |
| bordeaux.journal | International Mathematics Research Notices | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01904735 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01904735v1 | |
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