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Local spectral gap in the group of Euclidean isometries
Language
en
Article de revue
This item was published in
International Mathematics Research Notices. 2018-03-12
Oxford University Press (OUP)
English Abstract
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, ...Read more >
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].Read less <
Origin
Hal imported