| 宋 帅.可定向闭曲面上保定向的周期映射[J].数学年刊A辑,2016,37(4):433~450 |
| 可定向闭曲面上保定向的周期映射 |
| Orientation Preserving Periodic Maps on Orientable Closed Surfaces |
| Received:April 21, 2014 Revised:December 11, 2015 |
| DOI： |
| 中文关键词: 闭曲面, 可定向, 周期映射, 保定向, 共轭类 |
| 英文关键词:Closed surface, Orientable, Periodic map, Orientation preserving, Conjugate classes |
| 基金项目:本文受到首都师范大学研究生学术创新基金的资助. |
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| 中文摘要: |
| 讨论可定向闭曲面上保定向周期映射的共轭类分类问题. Kulkarni (1997)指出:
亏格$g$大于$3$时, 曲面上任意周期大于或等于$4g$的周期映射共轭于两类周期映射中某个映射的幂.
之后Hirose (2010)得到: 亏格$g$大于$12$时,
曲面上任意周期大于或等于$3g$的周期映射共轭于4类周期映射中某个映射的幂.
本文在此基础上研究了周期大于或等于$3(g-1)$的情形: 当亏格$g$大于$21$时,
得到了和Hirose相似的结论, 且找出了更多不能被包含在前面所讲的4类周期映射中的情形. |
| 英文摘要: |
| The author investigates the classification of the conjugate classes of
orientation preserving periodic maps on orientable closed surfaces. Kulkarni (1997) showed
that if $g$ is greater than $3$, any periodic map on the oriented surface of genus
$g$ with period more than or equal to $4g$ is conjugate to a power of two types of
periodic maps. After then Hirose (2010) showed that if $g$ is greater than $12$, any periodic
map on the surface with period more than or equal to $3g$ is conjugate to a power of one
of four types of periodic maps. Following the work of Kulkarni and Hirose, the author gets the
similar conclusion of Hirose's when $g$ is greater than $21$ if the period is more than
or equal to $3(g-1)$. On this condition the author can find more cases which are not included
in the four types of periodic maps. |
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