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

@misc{liu2026groupoid,
  title = {{Groupoid strict comparison for Ample Groupoids: Fiberwise Supramenability and Topological Amenability}},
  author = {Chunlin Liu and Xin Ma and Jianchao Wu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.08511},
  eprint = {2610.08511},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.08511},
}

TY  - UNPB
TI  - Groupoid strict comparison for Ample Groupoids: Fiberwise Supramenability and Topological Amenability
AU  - Chunlin Liu
AU  - Xin Ma
AU  - Jianchao Wu
PY  - 2026
DA  - 2026/10/06
PB  - arXiv
DO  - 10.48550/arxiv.2610.08511
UR  - https://arxiv.org/abs/2610.08511
AB  - 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 𝒢, we show that if 𝒢 is fiberwise supramenable or topologically amenable, then the clopen type semigroup S(𝒢) is almost unperforated. Consequently, if 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.
ER  -