2 citations · 5 across the 13 of their papers we have counts for
13 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…
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…
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…
Hyperfiniteness and Borel asymptotic dimension of boundary actions of hyperbolic groups
Petr Naryshkin, Andrea Vaccaro
We give a new short proof of the theorem due to Marquis and Sabok, which states that the orbit equivalence relation induced by the action of a finitely generated hyperbolic group o…
Group extensions preserve almost finiteness
Petr Naryshkin
We show that a free action is almost finite if its restriction to some infinite normal subgroup of is almost finite. Consider the class of groups which c…
Tracially amenable actions and purely infinite crossed products
Eusebio Gardella, Shirly Geffen, Julian Kranz +2
We introduce the notion of tracial amenability for actions of discrete groups on unital, tracial C-algebras, as a weakening of amenability where all the relevant approximations…
Dynamical comparison and -stability for crossed products of simple -algebras
Eusebio Gardella, Shirly Geffen, Petr Naryshkin +1
We establish -stability for crossed products of outer actions of amenable groups on -stable -algebras under a mild technical assumption which we call…
Classifiability of crossed products by nonamenable groups
Eusebio Gardella, Shirly Geffen, Julian Kranz +1
We show that all amenable, minimal actions of a large class of nonamenable countable groups on compact metric spaces have dynamical comparison. This class includes all nonamenable…
Polynomial growth, comparison, and the small boundary property
Petr Naryshkin
We show that a minimal action of a finitely generated group of polynomial growth on a compact metrizable space has comparison. It follows that if such an action has the small bound…
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…
Abundance of entire solutions to nonlinear elliptic equations by the variational method
L. M. Lerman, P. E. Naryshkin, A. I. Nazarov
We study entire bounded solutions to the equation in . Our approach is purely variational and is based on concentration arguments and symmetry consi…