Year: 2026
Type: preprint
Abstract: We investigate étale Hausdorff groupoids whose source fibres have controlled growth with respect to a length function. Our first result shows that uniform subexponential growth implies topological amenability. If the unit space is compact and metrizable and such a length satisfies a suitable uniform doubling condition, then the groupoid has weak $m$-comparison for some $m$. For minimal ample groupoids, this implies comparison and almost unperforation of the type semigroup. Under the additional assumption that the unit space has no isolated points, we deduce Matui's AH-conjecture.
Source: arXiv (Cornell University)
Authors: Austad, Are, Bönicke, Christian
Institution: University of Oslo
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7161565620