3 results
Continuum of allosteric actions for non-amenable surface groups
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- Journal:
- Ergodic Theory and Dynamical Systems / Volume 44 / Issue 6 / June 2024
- Published online by Cambridge University Press:
- 19 July 2023, pp. 1581-1596
- Print publication:
- June 2024
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Let
$\Sigma $ be a closed surface other than the sphere, the torus, the projective plane or the Klein bottle. We construct a continuum of probability measure preserving ergodic minimal profinite actions for the fundamental group of 
$\Sigma $ that are topologically free but not essentially free, a property that we call allostery. Moreover, the invariant random subgroups we obtain are pairwise distincts.
Amenable purely infinite actions on the non-compact Cantor set
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- Journal:
- Ergodic Theory and Dynamical Systems / Volume 40 / Issue 6 / June 2020
- Published online by Cambridge University Press:
- 20 November 2018, pp. 1619-1633
- Print publication:
- June 2020
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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].
Isometric Group Actions on Hilbert Spaces: Structure of Orbits
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- Journal:
- Canadian Journal of Mathematics / Volume 60 / Issue 5 / October 2008
- Published online by Cambridge University Press:
- 20 November 2018, pp. 1001-1009
- Print publication:
- October 2008
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