- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:48
Revista Matemática Iberoamericana
Rev. Mat. Iberoamericana
RMI
0213-2230
2235-0616
General
10.4171/RMI
http://www.ems-ph.org/doi/10.4171/RMI
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2012)
31
2015
4
Symmetries of quasiplatonic Riemann surfaces
Gareth
Jones
University of Southampton, SOUTHAMPTON, UNITED KINGDOM
David
Singerman
University of Southampton, SOUTHAMPTON, UNITED KINGDOM
Paul
Watson
Peter Symonds College, WINCHESTER, UNITED KINGDOM
Riemann surface, symmetry, triangle group, hypermap
We state and prove a corrected version of a theorem of Singerman, which relates the existence of symmetries (anticonformal involutions) of a quasiplatonic Riemann surface $\mathcal S$ (one uniformised by a normal subgroup $N$ of finite index in a cocompact triangle group $\Delta$) to the properties of the group $G=\Delta/N$. We give examples to illustrate the revised necessary and sufficient conditions for the existence of symmetries, and we relate them to properties of the associated dessins d'enfants, or hypermaps.
Functions of a complex variable
Combinatorics
Algebraic geometry
Group theory and generalizations
1403
1414
10.4171/RMI/873
http://www.ems-ph.org/doi/10.4171/RMI/873