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Amenable purely infinite actions on the non-compact Cantor set

Published online by Cambridge University Press:  20 November 2018

GÁBOR ELEK*
Affiliation:
Department of Mathematics And Statistics, Fylde College, Lancaster University, Lancaster, LA1 4YF, UK email [email protected]

Abstract

We prove that any countable non-amenable group $\unicode[STIX]{x1D6E4}$ admits a free, minimal, amenable, purely infinite action on the non-compact Cantor set. This answers a question of Kellerhals, Monod and Rørdam [Non-supramenable groups acting on locally compact spaces. Doc. Math.18 (2013), 1597–1626].

Type
Original Article
Copyright
© Cambridge University Press, 2018

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