6 papers
Quantitative orbit equivalence for rank-one systems
Corentin Correia, Spyridon Petrakos
We prove that any two rank-one systems are sub- orbit equivalent, fully clarifying quantitative orbit equivalence for a generic class of transformations. As a corollary, we es…
Topological full groups and stable rank one
David Kerr, Spyridon Petrakos
We establish stable rank one for the reduced group C-algebras of the C-simple topological full groups and dynamical alternating groups constructed by Kerr and Tucker-Drob.…
Quantitative orbit equivalence for -odometers
Petr Naryshkin, Spyridon Petrakos
We prove that any two -odometers are sub--orbit equivalent, greatly strengthening previous results and giving a definitive picture of quantitative orbit equivalenc…
Bauer simplices and the small boundary property
David Kerr, Grigoris Kopsacheilis, Spyridon Petrakos
We show that, for every minimal action of a countably infinite discrete group on a compact metrizable space, if the extreme boundary of the simplex of invariant Borel probability m…
Almost finiteness and groups of dynamical origin
Petr Naryshkin, Spyridon Petrakos
We introduce the property of having good subgroups for actions of countable discrete groups on compact metrizable spaces, and show that it implies comparison when the acting group…
McDuff factors from amenable actions and dynamical alternating groups
David Kerr, Spyridon Petrakos
Given a topologically free action of a countably infinite amenable group on the Cantor set, we prove that, for every subgroup of the topological full group containing the alter…