Embedding compact surfaces into the 3-dimensional Euclidean space with maximum symmetry

The symmetries of surfaces which can be embedded into the symmetries of the 3-dimensional Euclidean space R3 are easier to feel by human's intuition. We give the maximum order of finite group actions on (R3 E) among all possible embedded closed/bordered surfaces with given geometric/algebraic genus...

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Veröffentlicht in:Science China. Mathematics 2017-09, Vol.60 (9), p.1599-1614
Hauptverfasser: Wang, Chao, Wang, ShiCheng, Zhang, YiMu, Zimmermann, Bruno
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description The symmetries of surfaces which can be embedded into the symmetries of the 3-dimensional Euclidean space R3 are easier to feel by human's intuition. We give the maximum order of finite group actions on (R3 E) among all possible embedded closed/bordered surfaces with given geometric/algebraic genus greater than 1 in R3. We also identify the topological types of the bordered surfaces realizing the maximum order, and findsimple representative embeddings for such surfaces.
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subjects Applications of Mathematics
Euclidean geometry
Euclidean space
Mathematics
Mathematics and Statistics
三维欧氏空间
三维立体空间
对称性
嵌入
拓扑类型
曲面
群作用
表面
title Embedding compact surfaces into the 3-dimensional Euclidean space with maximum symmetry
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