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arXiv · 2306.01633

Monodromy Groups of Dessins d'Enfant on Rational Polygonal Billiards Surfaces

Richard A. Moy·Jason Schmurr·Japheth Varlack
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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. In this paper, 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.

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Richard A. Moy, Jason Schmurr, Japheth Varlack. 2023-06-02. Monodromy Groups of Dessins d'Enfant on Rational Polygonal Billiards Surfaces. https://arxiv.org/abs/2306.01633

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