6 papers
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…
Hyper-u-amenablity and Hyperfiniteness of Treeable Equivalence Relations
Petr Naryshkin, Andrea Vaccaro
We introduce the notions of u-amenability and hyper-u-amenability for countable Borel equivalence relations, strong forms of amenability that are implied by hyperfiniteness. We sho…
Elementary amenability and almost finiteness
David Kerr, Petr Naryshkin
We show that every free continuous action of a countably infinite elementary amenable group on a finite-dimensional compact metrizable space is almost finite. As a consequence, the…
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…
URP, comparison, mean dimension, and sharp shift embeddability
Petr Naryshkin
For a free action of an amenable group on a compact metrizable space, we study the Uniform Rokhlin Property (URP) and the conjunction of Uniform Rokhlin Prop…
Essential freeness, allostery and -stability of crossed products
Eusebio Gardella, Shirly Geffen, Rafaela Gesing +2
We explore classifiability of crossed products of actions of countable amenable groups on compact, metrizable spaces. It is completely understood when such crossed products are sim…