Branched Covers of Open Manifolds
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908698914324480 |
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| author | Hughes, Mark Kjuchukova, Alexandra Miller, Maggie |
| author_facet | Hughes, Mark Kjuchukova, Alexandra Miller, Maggie |
| contents | For $m=2$ and $m=3$ we prove that any connected, oriented, open manifold $M^m$ admits a simple branched covering map over $\mathbb{R}^m$. When $M$ has $k$ ends and $k$ is finite, the degree of the cover can be taken to be $mk$. Regardless of the number of ends, $M$ admits a branched covering map of countably infinite degree over $\mathbb{R}^m$. We also investigate which compact manifolds are universal bases, that is, are branch covered by all compact manifolds in the same dimension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_09842 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Branched Covers of Open Manifolds Hughes, Mark Kjuchukova, Alexandra Miller, Maggie Geometric Topology 57M12 (Primary) 57M10 (Secondary) For $m=2$ and $m=3$ we prove that any connected, oriented, open manifold $M^m$ admits a simple branched covering map over $\mathbb{R}^m$. When $M$ has $k$ ends and $k$ is finite, the degree of the cover can be taken to be $mk$. Regardless of the number of ends, $M$ admits a branched covering map of countably infinite degree over $\mathbb{R}^m$. We also investigate which compact manifolds are universal bases, that is, are branch covered by all compact manifolds in the same dimension. |
| title | Branched Covers of Open Manifolds |
| topic | Geometric Topology 57M12 (Primary) 57M10 (Secondary) |
| url | https://arxiv.org/abs/2508.09842 |