Filippo Calderoni : Borel structures on the space of left-orderings

Posted by Filippo Calderoni , part of the Logic Seminar.

At

Feb. 18, 2020, 3 p.m.

In

427 SEO

Abstract

In this work we address a question of Deroin, Navas, and Rivas. We discuss how descriptive set theory can be used to find many examples of countable left-orderable groups such that the quotient space \(\mathrm{LO}(G)/G\) is not standard. Moreover, we prove that the countable Borel equivalence relation induced from the conjugacy action of \(\mathbb{F}_{2}\) on \(\mathrm{LO}(\mathbb{F}_{2})\) is universal. This is joint work with Adam Clay.