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

2024/08/25 by Wang Chao, Wang, Chao, Shicheng Wang +3 · 1 citation
Mathematics · Computer Science · #Mathematical Dynamics and Fractals #Computational Geometry and Mesh Generation #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2408.13749

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≥ 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.

Cited by

• Equivariant embeddings of Riemann surfaces in Euclidean spaces with minimal dimensions

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