MONODROMY GROUPS OF DESSINS D’ENFANT ON RATIONAL POLYGONAL BILLIARDS SURFACES

Rocky Mountain Journal of Mathematics 2026 Open access

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Authors: Richard A. Moy, Jason Schmurr, Japheth Varlack
DOI: 10.1216/rmj.2026.56.475
Cited by: 0

Abstract

A dessin d’enfant, or dessin, is a bicolored graph embedded into a Riemann surface, and the monodromy group is an algebraic invariant of the dessin generated by rotations of edges about black and white vertices. A rational polygonal billiards surface is a Riemann surface that arises from the dynamical system of billiards within a rational-angled polygon. We compute the monodromy groups of dessins embedded into rational polygonal billiards surfaces and identify all possible monodromy groups arising from rational triangular billiards surfaces.

Fields of Study & Subjects

Mathematics and Applications Geometric and Algebraic Topology Mathematical Dynamics and Fractals

Publication details

Journal / source
Rocky Mountain Journal of Mathematics
Volume
56
Issue
2
Pages
475–501
Publication date
1 April 2026
Language
EN