On the dynamic asymptotic dimension of étale groupoids
arXiv:2307.07309 · doi:10.1007/s00209-024-03492-x
Abstract
We investigate the dynamic asymptotic dimension for étale groupoids introduced by Guentner, Willett and Yu. In particular, we establish several permanence properties, including estimates for products and unions of groupoids. We also establish invariance of the dynamic asymptotic dimension under Morita equivalence. In the second part of the article, we consider a canonical coarse structure on an étale groupoid and compare the asymptotic dimension of the resulting coarse space with the dynamic asymptotic dimension of the underlying groupoid.
20 pages, some small corrections, Example 3.2 and Remark 3.10 were added to the manuscript