Counting the number of quasiplatonic topological actions of the cyclic group on surfaces

Charles Camacho

doi:10.1216/rmj.2020.50.1221

Abstract

We derive a closed formula for the number of quasiplatonic topological actions of the cyclic group on surfaces of genus two or greater. The formula implies that the number of quasiplatonic cyclic group actions is roughly one-sixth the number of regular dessins d’enfants with a cyclic group of automorphisms.

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Charles Camacho. "Counting the number of quasiplatonic topological actions of the cyclic group on surfaces." Rocky Mountain J. Math. 50 (4) 1221 - 1239, August 2020. https://doi.org/10.1216/rmj.2020.50.1221

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Received: 9 August 2019; Accepted: 27 January 2020; Published: August 2020

First available in Project Euclid: 29 September 2020

zbMATH: 07261861

MathSciNet: MR4154804

Digital Object Identifier: 10.1216/rmj.2020.50.1221

Subjects:

Primary: 57M60

Secondary: 14H57 , 30F99

Keywords: Belyi's theorem , cyclic group , dessins , dessins d'enfants , Grothendieck , group actions , Harvey's theorem , Riemann surfaces

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