BOUTONNET, Rémi; IOANA, Adrian

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BOUTONNET, Rémi
Institut de Mathématiques de Bordeaux [IMB]

IOANA, Adrian
Mathematics Department; University of California San Diego

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International Mathematics Research Notices. 2018-03-12

Oxford University Press (OUP)

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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].< Réduire

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Local spectral gap in the group of Euclidean isometries

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