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arXiv · 2605.16013

Amenability and comparison for étale groupoids with polynomial growth

Are Austad·Christian Bönicke
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Abstract

We show that any second-countable locally compact Hausdorff étale groupoid with polynomial growth is topologically amenable. If moreover the groupoid is compactly generated with compact and metrizable unit space, it has weak $m$-comparison. Thus if the groupoid is also ample and minimal, it satisfies Matui's AH-conjecture.

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Are Austad, Christian Bönicke. 2026-06-08. Amenability and comparison for étale groupoids with polynomial growth. https://arxiv.org/abs/2605.16013

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