Revista Matemática Iberoamericana
- Rev. Mat. Iberoamericana
- Volume 24, Number 3 (2008), 921-939.
Reflections of regular maps and Riemann surfaces
A compact Riemann surface of genus $g$ is called an M-surface if it admits an anti-conformal involution that fixes $g+1$ simple closed curves, the maximum number by Harnack's Theorem. Underlying every map on an orientable surface there is a Riemann surface and so the conclusions of Harnack's theorem still apply. Here we show that for each genus $g ϯ 1$ there is a unique M-surface of genus $g$ that underlies a regular map, and we prove a similar result for Riemann surfaces admitting anti-conformal involutions that fix $g$ curves.
Rev. Mat. Iberoamericana, Volume 24, Number 3 (2008), 921-939.
First available in Project Euclid: 9 December 2008
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Melekoğlu, Adnan; Singerman, David. Reflections of regular maps and Riemann surfaces. Rev. Mat. Iberoamericana 24 (2008), no. 3, 921--939. https://projecteuclid.org/euclid.rmi/1228834298