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
投稿时间: 2014-04-21  最后修改时间: 2015-12-11
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.
作者单位
宋 帅 首都师范大学数学科学学院, 北京 100048. 
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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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