Mapping class groups of solenoidal manifolds

The goal of this work is to calculate the mapping class groups of solenoidal manifolds. We introduce the dynamical commensurator group associated to an odometer action, and develop methods to calculate the mapping class group using the dynamical commensurator. Our results generalize the previous results of Odden for the mapping class group of the universal solenoid over a Riemann surface, and of Bering and Studenmund for the pointed mapping class group of the universal solenoid over a compact aspherical manifold. We include a selection of examples.