Filippo Calderoni : Rotation equivalence and superrigidity

Posted by Filippo Calderoni , part of the Logic Seminar.

At

Feb. 22, 2022, 4 p.m.

In

636 SEO

Abstract

The theory of countable Borel equivalence relations (CBERs) analyzes the actions of countable groups. The main question is how much information is encoded by the orbit space. The more information is encoded the more rigid the action is. We prove rigidity results for the action of the group of rational rotations on spheres in higher dimension. This connects to superrigidity in work by Margulis and to Zimmer's program about the actions of discrete subgroups of Lie groups on manifolds. Moreover, our methods provide new examples of CBERs, and a new proof of a fundamental theorem of Adams and Kechris about Borel complexity.