Kurt Gödel Research Center

2015 seminar talk: Strong treeability of planar groups

Talk held by Clinton Conley (Cornell University, New York, USA) at the KGRC seminar on 2015-06-11.

Abstract

An equivalence relation is called treeable if it can be realized as the connectedness relation of an acyclic Borel graph. We call a finitely generated group planar if there is some finite generating set such that the induced Cayley graph of the group is planar. Using techniques originally created to analyze measure-theoretic chromatic numbers of graphs, we show that any orbit equivalence relation of a free measure-preserving action of a planar group on a standard probability space is treeable on a conull set.

This is joint work with Gaboriau, Marks, and Tucker-Drob.