2023/06/02 by Moy, Richard A., Schmurr, Jason, Varlack, Japheth
#FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2306.01633
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.