Compact aspherical solenoids
Geometric Topology
2025-07-02 v4 Algebraic Topology
Abstract
We consider compact, aspherical solenoids obtained as the inverse limit of a system of CW~complexes and covering maps. This includes -adic solenoids, as well as the universal hyperbolic solenoid of Teichm\"{u}ller 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.
Cite
@article{arxiv.1009.5716,
title = {Compact aspherical solenoids},
author = {James Belk and Bradley Forrest},
journal= {arXiv preprint arXiv:1009.5716},
year = {2025}
}
Comments
This is a revision of our 2011 preprint entitled "Covering systems, solenoids, and shape theory". The error has been corrected