科研之友
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摘要
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.
- 出版日期2016-10
