Embedding periodic maps of surfaces into those of spheres with minimal dimensions
Abstract
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 $k$.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2024
- DOI:
- 10.48550/arXiv.2408.13749
- arXiv:
- arXiv:2408.13749
- Bibcode:
- 2024arXiv240813749W
- Keywords:
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- Mathematics - Geometric Topology;
- Primary 57R40;
- Secondary 57M12;
- 57M60
- E-Print:
- 20 pages, 8 Figures