Embedding periodic maps of surfaces into those of spheres with minimal dimensions

Chao Wang; Shicheng Wang; Zhongzi Wang

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arXiv · 2408.13749

Embedding periodic maps of surfaces into those of spheres with minimal dimensions

Chao Wang·Shicheng Wang·Zhongzi Wang

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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 $k$.

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Chao Wang, Shicheng Wang, Zhongzi Wang. 2024-08-25. Embedding periodic maps of surfaces into those of spheres with minimal dimensions. https://arxiv.org/abs/2408.13749

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