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arXiv · 2106.15588

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

Madison Mabe·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 billiards surface is a two dimensional surface that allows one to view the path of a billiards ball as a continuous path. In this paper, we classify the monodromy groups of dessins associated to rational triangular billiards surfaces.

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Madison Mabe, Richard A. Moy, Jason Schmurr, Japheth Varlack. 2021-06-29. Monodromy Groups of Dessins d'Enfant on Rational Triangular Billiards Surfaces. https://doi.org/10.2140/involve.2023.16.49

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