Embedding Periodic Maps on Surfaces into Those on S-3

作者：Guo Yu^*; Wang Chao; Wang Shicheng; Zhang Yimu

来源：Chinese Annals of Mathematics Series B, 2015, 36(2): 161-180.

DOI：10.1007/s11401-015-0890-z

• Symmetry of surface
• Symmetry of 3-sphere
• Extendable action

Call a periodic map h on the closed orientable surface Sigma(g) extendable if h extends to a periodic map over the pair (S-3, Sigma(g)) for possible embeddings e : Sigma(g) -> S-3. The authors determine the extendabilities for all periodical maps on Sigma(2). The results involve various orientation preserving/reversing behalves of the periodical maps on the pair (S-3, Sigma(g)). To do this the authors first list all periodic maps on Sigma(2), 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 Sigma(g) is extendable, which contrasts sharply with the situation in the orientation preserving category.

• 出版日期2015-3
• 单位北京大学