Steven Hurder; Professor Emeritus; Department of Mathematics; University of Illinois at Chicago
"Stable Cantor Dynamics"
Abstract: A Cantor dynamical system is the action of a finitely generated group G on a Cantor space X. The class of equicontinuous Cantor actions is equivalent to the class of arboreal actions. We discuss properties of the equicontinuous Cantor actions, and introduce the notion of a stable Cantor action. We define a new invariant of stable Cantor actions, the stable discriminant. A main result is that the stable discriminant is an invariant of continuous orbit equivalence of the action. We discuss examples provided by actions of nilpotent groups, and actions associated to non-co-Hopfian groups.