Uncountably many simple groups up to quasi-isometry

Abstract: The purpose of geometric group theory is to investigate groups up to quasi-isometry, a coarse geometric notion. Many classes of groups contain uncountably many finitely generated groups up to isomorphism. From a geometric perspective one is led to ask (for each class) whether this remains true up to quasi-isometry. I will talk about joint work with Ashot Minasyan and Denis Osin where we use the Baire category theorem to answer such questions. Specifically I will show that there are uncountably many finitely generated simple groups up to quasi-isometry.

algebraic topologydifferential geometrygeneral topologygroup theorygeometric topology

Audience: researchers in the topic

Ohio State Topology and Geometric Group Theory Seminar

Series comments: https://sites.google.com/view/topoandggt