arXiv subjects

Inessa Epstein

Publications and source records attributed to Inessa Epstein.

3 recordsLinked to original sources

arXiv2012

The Borel complexity of von Neumann equivalence

We prove that for a countable discrete group $Γ$ containing a copy of the free group $\F_n$, for some $2\leq n\leq\infty$, as a normal subgroup, the equivalence relations of conjugacy, orbit equivalence and von Neumann equivalence of the ergodic a.e. free actions of $Γ$ are analytic non-Borel equivalence relations in the Polish space of probability measure preserving $Γ$ actions. As a consequence we obtain that the isomorphism relation in the spaces of separably acting factors of type $\II_1$, $\II_\infty$ and $\III_λ$, $0\leqλ\leq 1$, are analytic and not Borel when these spaces are given the Effros Borel structure.

math.DS↗

arXiv2008

Non-unitarisable representations and random forests

We establish a connection between Dixmier's unitarisability problem and the expected degree of random forests on a group. As a consequence, a residually finite group is non-unitarisable if its first L2-Betti number is non-zero or if it is finitely generated with non-trivial cost. Our criterion also applies to torsion groups constructed by D. Osin, thus providing the first examples of non-unitarisable groups not containing a non-Abelian free subgroup.

math.GR↗

arXiv2008

Orbit inequivalent actions of non-amenable groups

Consider two free measure preserving group actions $Γ\actson (X, μ), Δ\actson (X, μ)$, and a measure preserving action $Δ\actson^a (Z, ν)$ where $(X, μ), (Z, ν)$ are standard probability spaces. We show how to construct free measure preserving actions $Γ\actson^c (Y, m)$, $Δ\actson^d (Y, m)$ on a standard probability space such that $E_Δ^d \subset E_Γ^c$ and $d$ has $a$ as a factor. This generalizes the standard notion of co-induction of actions of groups from actions of subgroups. We then use this construction to show that if $Γ$ is a countable non-amenable group, then $Γ$ admits continuum many orbit inequivalent free, measure preserving, ergodic actions on a standard probability space.

math.GR↗