Embedding periodic maps on surfaces into those on S 3
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- 作者：Yu Guo ; Chao Wang ; Shicheng Wang ; Yimu Zhang
- 关键词：Symmetry of surface ; Symmetry of 3 ; sphere ; Extendable action ; 57M60 ; 57S17 ; 57S25
- 刊名：Chinese Annals of Mathematics - Series B
- 出版年：2015
- 出版时间：March 2015
- 年：2015
- 卷：36
- 期：2
- 页码：161-180
- 全文大小：777 KB
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- 刊物主题：Mathematics
Mathematics
Applications of Mathematics
Chinese Library of Science - 出版者：Springer Berlin / Heidelberg
- ISSN：1860-6261
文摘
Call a periodic map h on the closed orientable surface Σ g extendable if h extends to a periodic map over the pair (S 3,Σ g ) for possible embeddings e: Σ g ?S 3. 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 (S 3,Σ g ). 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 Σ g is extendable, which contrasts sharply with the situation in the orientation preserving category.