Open Access
October, 2016 A uniqueness of periodic maps on surfaces
J. Math. Soc. Japan 68(4): 1777-1787 (October, 2016). DOI: 10.2969/jmsj/06841777


Kulkarni showed that, if $g$ is greater than $3$, a periodic map on an oriented surface $\Sigma_g$ of genus $g$ with order not smaller than $4g$ is uniquely determined by its order, up to conjugation and power. In this paper, we show that, if $g$ is greater than $30$, the same phenomenon happens for periodic maps on the surfaces with orders more than $8g/3$, and, for any integer $N$, there is $g > N$ such that there are periodic maps of $\Sigma_g$ of order $8g/3$ which are not conjugate up to power each other. Moreover, as a byproduct of our argument, we provide a short proof of Wiman's classical theorem: the maximal order of periodic maps of $\Sigma_g$ is $4g+2$.


Download Citation

Susumu HIROSE. Yasushi KASAHARA. "A uniqueness of periodic maps on surfaces." J. Math. Soc. Japan 68 (4) 1777 - 1787, October, 2016.


Published: October, 2016
First available in Project Euclid: 24 October 2016

zbMATH: 1375.57025
MathSciNet: MR3564451
Digital Object Identifier: 10.2969/jmsj/06841777

Primary: 57N05
Secondary: 20F38 , 57M60

Keywords: automorphism , cyclic group , Riemann surface

Rights: Copyright © 2016 Mathematical Society of Japan

Vol.68 • No. 4 • October, 2016
Back to Top