The symmetries of surfaces which can be embedded into the symmetries of the 3-dimensional Euclidean space R^3 are easier to feel by human's intuition. We give the maximum order of finite group actions on(R^3, Σ) ...The symmetries of surfaces which can be embedded into the symmetries of the 3-dimensional Euclidean space R^3 are easier to feel by human's intuition. We give the maximum order of finite group actions on(R^3, Σ) among all possible embedded closed/bordered surfaces with given geometric/algebraic genus greater than 1 in R^3. We also identify the topological types of the bordered surfaces realizing the maximum order, and find simple representative embeddings for such surfaces.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.11371034 and 11501239)
文摘The symmetries of surfaces which can be embedded into the symmetries of the 3-dimensional Euclidean space R^3 are easier to feel by human's intuition. We give the maximum order of finite group actions on(R^3, Σ) among all possible embedded closed/bordered surfaces with given geometric/algebraic genus greater than 1 in R^3. We also identify the topological types of the bordered surfaces realizing the maximum order, and find simple representative embeddings for such surfaces.
