Embedding compact surfaces into the 3-dimensional Euclidean space with maximum symmetry |
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| Authors: | Chao Wang ShiCheng Wang YiMu Zhang Bruno Zimmermann |
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| Institution: | 1.Jonsvannsveien 87B, H0201,Trondheim,Norway;2.School of Mathematical Sciences,Peking University,Beijing,China;3.Mathematics School,Jilin University,Changchun,China;4.Dipartimento di Matematica e Geoscienze,Universita degli Studi di Trieste,Trieste,Italy |
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| Abstract: | The symmetries of surfaces which can be embedded into the symmetries of the 3-dimensional Euclidean space ?3 are easier to feel by human’s intuition. We give the maximum order of finite group actions on (?3, Σ) among all possible embedded closed/bordered surfaces with given geometric/algebraic genus greater than 1 in ?3. We also identify the topological types of the bordered surfaces realizing the maximum order, and find simple representative embeddings for such surfaces. |
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