|
|
| |
| Embedding Periodic Maps on Surfaces into Those on S3 |
| |
Citation： |
Yu GUO,Chao WANG,Shicheng WANG,Yimu ZHANG.Embedding Periodic Maps on Surfaces into Those on S3[J].Chinese Annals of Mathematics B,2015,36(2):161~181 |
| Page view： 3605
Net amount： 2183 |
Authors： |
Yu GUO; Chao WANG; Shicheng WANG; Yimu ZHANG; |
Foundation： |
the National Natural Science Foundation of China (No. 10631060). |
|
|
| Abstract： |
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 $e: \Sigma_g\to S^3$. 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. |
Keywords： |
Symmetry of surface, Symmetry of 3-sphere, Extendable action |
Classification： |
57M60, 57S17, 57S25 |
|
|
Download PDF Full-Text
|
|
|
|
