2010/09/28 by Belk, James, Forrest, Bradley
#30F60 #37B45 (Secondary) #55P55 (Primary) 55P10 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.1009.5716
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.