Orientation Preserving Periodic Maps on Orientable Closed Surfaces

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 Hi rose'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.