Amenability and comparison for \'etale groupoids with polynomial growth
Dynamical Systems
2026-05-18 v1 Operator Algebras
Abstract
We show that any second-countable \'etale groupoid with polynomial growth is topologically amenable. If its unit space is compact and metrizable, we show that the groupoid has weak -comparison. Thus if the groupoid is also ample and minimal, it satisfies Matui's AH conjecture.
Keywords
Cite
@article{arxiv.2605.16013,
title = {Amenability and comparison for \'etale groupoids with polynomial growth},
author = {Are Austad and Christian Bönicke},
journal= {arXiv preprint arXiv:2605.16013},
year = {2026}
}
Comments
22 pages. Comments welcome