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arXiv · 2610.08511

Groupoid strict comparison for Ample Groupoids: Fiberwise Supramenability and Topological Amenability

Chunlin Liu·Xin Ma·Jianchao Wu
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Abstract

In this paper, we first introduce fiberwise supramenability for locally compact Hausdorff étale groupoids with compact unit space. Then, for such a minimal ample groupoid $\mathcal{G}$, we show that if $\mathcal{G}$ is fiberwise supramenable or topologically amenable, then the clopen type semigroup $S(\mathcal{G})$ is almost unperforated. Consequently, if $\mathcal{G}$ is $σ$-compact, then it has groupoid strict comparison. We then present several applications, including Matui's AH conjecture and pure infiniteness for groupoids and groupoid $C^*$-algebras.

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Chunlin Liu, Xin Ma, Jianchao Wu. 2026-10-06. Groupoid strict comparison for Ample Groupoids: Fiberwise Supramenability and Topological Amenability. https://arxiv.org/abs/2610.08511

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