Amenable purely infinite actions on the non-compact Cantor set

Elek, Gabor (2020) Amenable purely infinite actions on the non-compact Cantor set. Ergodic Theory and Dynamical Systems, 40 (6). pp. 1619-1633. ISSN 0143-3857

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Abstract

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