Compact aspherical solenoids

Abstract

We consider compact, aspherical solenoids obtained as the inverse limit of a system of CW~complexes and covering maps. This includes $P$-adic solenoids, as well as the universal hyperbolic solenoid of Teichmüller theory. Using ideas from shape theory, we classify maps between such solenoids up to homotopy, and we prove a Dehn-Nielsen-type theorem for self-homotopy equivalences of such a solenoid. This generalizes a result of Odden regarding the universal hyperbolic solenoid.

This is a revision of our 2011 preprint entitled "Covering systems, solenoids, and shape theory". The error has been corrected