A characterization of proper actions with bornology and coarse geometry
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915259877425152 |
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| author | Nagaya, Hiroaki |
| author_facet | Nagaya, Hiroaki |
| contents | In 1961, Palais showed that every smooth proper Lie group action on a smooth manifold admits a compatible Riemannian metric on the manifold such that the action becomes isometric. In 2006, Yoshino studied a continuous proper action of a locally compact Hausdorff group on a locally compact Hausdorff space, and showed that the space carries a compatible uniform structure making the action equi continuous in an appropriate setting. In this paper, we focus on bornological proper actions on bornological spaces and prove that the space admits a compatible coarse structure such that the action becomes equi controlled. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_18811 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A characterization of proper actions with bornology and coarse geometry Nagaya, Hiroaki Differential Geometry General Topology 57S30, 46A08, 46A17, 53C23, 51F30 In 1961, Palais showed that every smooth proper Lie group action on a smooth manifold admits a compatible Riemannian metric on the manifold such that the action becomes isometric. In 2006, Yoshino studied a continuous proper action of a locally compact Hausdorff group on a locally compact Hausdorff space, and showed that the space carries a compatible uniform structure making the action equi continuous in an appropriate setting. In this paper, we focus on bornological proper actions on bornological spaces and prove that the space admits a compatible coarse structure such that the action becomes equi controlled. |
| title | A characterization of proper actions with bornology and coarse geometry |
| topic | Differential Geometry General Topology 57S30, 46A08, 46A17, 53C23, 51F30 |
| url | https://arxiv.org/abs/2504.18811 |