可定向闭曲面上保定向的周期映射

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.

Orientation Preserving Periodic Maps on Orientable Closed Surfaces

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.