Compact aspherical solenoids

James Belk; Bradley Forrest

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arXiv · 1009.5716

Compact aspherical solenoids

James Belk·Bradley Forrest

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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 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.

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James Belk, Bradley Forrest. 2010-09-28. Compact aspherical solenoids. https://arxiv.org/abs/1009.5716

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