Embedding Periodic Maps on Surfaces into Those on S^3

作     者：Yu GUO Chao WANG Shicheng WANG Yimu ZHANG 

作者机构：School of Mathematical Sciences Peking University 

出 版 物：《Chinese Annals of Mathematics,Series B》 (数学年刊（B辑英文版）)

年 卷 期：2015年第36卷第2期

页      面：161-180页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by the National Natural Science Foundation of China(No.10631060) 

主　　题：Symmetry of surface Symmetry of 3-sphere Extendable action 

摘      要：Call a periodic map h on the closed orientable surface Σg extendable if h extends to a periodic map over the pair(S3, Σg) for possible embeddings e : Σg→ S3. The authors determine the extendabilities for all periodical maps on Σ2. The results involve various orientation preserving/reversing behalves of the periodical maps on the pair(S3, Σg). To do this the authors first list all periodic maps on Σ2, and indeed the authors exhibit each of them as a composition of primary and explicit symmetries, like rotations, reflections and antipodal maps, which itself should be interesting. A by-product is that for each even g,the maximum order periodic map on Σg is extendable, which contrasts sharply with the situation in the orientation preserving category.