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Mathematics > Geometric Topology

arXiv:1411.7728 (math)
[Submitted on 28 Nov 2014 (v1), last revised 10 Feb 2015 (this version, v2)]

Title:A uniqueness of periodic maps on surfaces

Authors:Susumu Hirose, Yasushi Kasahara
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Abstract:Kulkarni showed that, if g is greater than 3, a periodic map on an oriented surface S_g of genus g with order more than or equal to 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 S_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 S_g is 4g+2.
Comments: 13 pages, no figure; minor changes in exposition, and typos corrected
Subjects: Geometric Topology (math.GT)
Cite as: arXiv:1411.7728 [math.GT]
  (or arXiv:1411.7728v2 [math.GT] for this version)
  https://doi.org/10.48550/arXiv.1411.7728

Submission history

From: Susumu Hirose [view email]
[v1] Fri, 28 Nov 2014 00:47:23 UTC (9 KB)
[v2] Tue, 10 Feb 2015 06:37:05 UTC (9 KB)
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