可定向闭曲面上最大阶保定向周期映射的唯一性

Uniqueness of Orientation Preserving Periodic Maps of Maximal Order on Orientable Closed Surfaces

A. Wiman和W. J. Harvey证明了在亏格为g,g≥2的可定向闭曲面上,保定向周期自同胚的最大阶是4g+2。本文中我们研究了这样的映射的唯一性。我们证明曲面的自同构群的由这样的映射生成的4g+2阶循环子群在共轭意义下是唯一的。

It was proved by A. Wiman and W. J. Harvey that the maximal order of an orientation preserving Periodic map on an orientable closed surface of genus g. g≥2, is 4g + 2. In this paper, we investigate the uniqueness of such maps. We prove that the cyclic group of order 4g + 2 generated by such a map is unique up to conjugacy in the group of automorphisms of the surface.