Embedding periodic maps of surfaces into those of spheres with minimal dimensions
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913479160496128 |
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| author | Wang, Chao Wang, Shicheng Wang, Zhongzi |
| author_facet | Wang, Chao Wang, Shicheng Wang, Zhongzi |
| contents | It is known that any periodic map of order $n$ on a closed oriented surface of genus $g$ can be equivariantly embedded into $S^m$ for some $m$. In the orientable and smooth category, we determine the smallest possible $m$ when $n\geq 3g$. We show that for each integer $k>1$ there exist infinitely many periodic maps such that the smallest possible $m$ is equal to $k$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_13749 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Embedding periodic maps of surfaces into those of spheres with minimal dimensions Wang, Chao Wang, Shicheng Wang, Zhongzi Geometric Topology Primary 57R40, Secondary 57M12, 57M60 It is known that any periodic map of order $n$ on a closed oriented surface of genus $g$ can be equivariantly embedded into $S^m$ for some $m$. In the orientable and smooth category, we determine the smallest possible $m$ when $n\geq 3g$. We show that for each integer $k>1$ there exist infinitely many periodic maps such that the smallest possible $m$ is equal to $k$. |
| title | Embedding periodic maps of surfaces into those of spheres with minimal dimensions |
| topic | Geometric Topology Primary 57R40, Secondary 57M12, 57M60 |
| url | https://arxiv.org/abs/2408.13749 |