Topological Rigidity of the Dynamic Asymptotic Dimension

Abstract

We show for a free action of a countable group $\Gamma$ on a finite-dimensional, compact metric space by homeomorphisms that the dynamic asymptotic dimension is either infinite or coincides with the asymptotic dimension of $\Gamma$.

arXiv comment12 pages, comments welcome v2 corrected a mistake in the proof of the main result v3 fixed some typos and other minor details, v4 fixed many more small typos and a small mistake in the main theorem, v5 changed Lemma 2.8 to fix a mistake and adjusted the proof of the main theorem accordingly