6 papers
Classification of Fuchsian groups with torsion
George Peterzil
In their recent paper, Bergfalk and Smythe prove that the isometry equivalence relation on hyperbolic surfaces with finitely-generated fundamental group is concretely classifiable,…
Wasserstein stability and the nonsingular Borel lifting problem
Nachi Avraham-Re'em, George Peterzil
The Borel lifting problem asks when a nonsingular near action of a Polish group can be represented by a genuine Borel action. For locally compact Polish groups, a classical theorem…
The Hopf decomposition of locally compact group actions
Nachi Avraham-Re'em, George Peterzil
We develop a unified approach to the classical Hopf Decomposition (also known as the conservative--dissipative decomposition) for actions of locally compact second countable groups…
Cofinal families of finite VC-dimension
Omer Ben-Neria, Itay Kaplan, George Peterzil
Given infinite cardinals , we ask for the minimal VC-dimension of a cofinal family . We show that for and it is con…
Uncountable Hyperfiniteness and The Random Ratio Ergodic Theorem
Nachi Avraham-Re'em, George Peterzil
We show that the orbit equivalence relation of a free action of a locally compact group is hyperfinite (Ã la Connes-Feldman-Weiss) precisely when it is 'hypercompact'. This implies…
Irrationality of the Length Spectrum
George Peterzil, Guy Sapire
It is a classical result of Dal'Bo that the length spectrum of a non-elementary Fuchsian group is non-arithmetic, namely, it generates a dense additive subgroup of . In…