Amenable Purely Infinite Actions on the Non-Compact Cantor Set

Ergodic theory and dynamical systems/Ergodic theory & dynamical systems（2018）

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摘要

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].

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