Geometry, Topology and Dynamics Seminar
Steve Hurder
UIC
Dynamical Commensurator Groups
Abstract: We introduce the dynamical commensurator group for a generalized odometer action, that is for minimal equicontinuous group actions on Cantor sets. We show there is a map from the pointed mapping class group of a solenoidal manifold (ie a weak solenoid) to a dynamical commensurator group, and give conditions for when this map is either surjective or an isomorphism. Odden proved that this map is an isomorphism for the mapping class of the universal hyperbolic solenoid; Bering and Studenmund proved that the mapping class group of a universal solenoid over a compact K(G,1) manifold maps onto the commensurator group of G. We extend the results of both of these papers to arbitrary solenoidal manifolds. This work is joint with Olga Lukina.
Wednesday October 29, 2025 at 3:00 PM in 636 SEO