Amenability and comparison for étale groupoids with polynomial growth
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866913132590399488 |
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| author | Austad, Are Bönicke, Christian |
| author_facet | Austad, Are Bönicke, Christian |
| contents | We show that any second-countable étale groupoid with polynomial growth is topologically amenable. If its unit space is compact and metrizable, we show that the groupoid has weak $m$-comparison. Thus if the groupoid is also ample and minimal, it satisfies Matui's AH conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_16013 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Amenability and comparison for étale groupoids with polynomial growth Austad, Are Bönicke, Christian Dynamical Systems Operator Algebras 22A22, 37B05, 43A07 We show that any second-countable étale groupoid with polynomial growth is topologically amenable. If its unit space is compact and metrizable, we show that the groupoid has weak $m$-comparison. Thus if the groupoid is also ample and minimal, it satisfies Matui's AH conjecture. |
| title | Amenability and comparison for étale groupoids with polynomial growth |
| topic | Dynamical Systems Operator Algebras 22A22, 37B05, 43A07 |
| url | https://arxiv.org/abs/2605.16013 |