Groupoid strict comparison for Ample Groupoids: Fiberwise Supramenability and Topological Amenability
Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Liu, Chunlin, Ma, Xin, Wu, Jianchao
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220905037