Abstract
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, Σ) 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 find simple representative embeddings for such surfaces.
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This work was supported by National Natural Science Foundation of China (Grant Nos. 11371034 and 11501239).
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Dedicated to Professor Boju Jiang on the Occasion of His 80th Birthday
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Wang, C., Wang, S., Zhang, Y. et al. Embedding compact surfaces into the 3-dimensional Euclidean space with maximum symmetry. Sci. China Math. 60, 1599–1614 (2017). https://doi.org/10.1007/s11425-017-9078-0
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DOI: https://doi.org/10.1007/s11425-017-9078-0