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Monodromy
groups of dessins d'enfant on rational triangular billiards
surfaces
Madison Mabe, Richard A. Moy, Jason Schmurr and Japheth Varlack |
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Vol. 16 (2023), No. 1, 49–58
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Abstract |
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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. We classify the monodromy groups of dessins associated to rational triangular billiards surfaces. |
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Keywords
dessins d'enfant, monodromy groups, triangular billiards
surface
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Mathematical Subject Classification
Primary: 11G32, 14H57
Secondary: 37C83
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Milestones
Received: 14 July 2021
Revised: 5 March 2022
Accepted: 23 March 2022
Published: 14 April 2023
Communicated by Nathan Kaplan
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Authors |
| Madison Mabe | |
| Department of Mathematical
Sciences Lee University Cleveland, TN United States |
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| Richard A. Moy | |
| Department of Mathematical
Sciences Lee University Cleveland, TN United States |
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| Jason Schmurr | |
| Department of Mathematical
Sciences Lee University Cleveland, TN United States |
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| Japheth Varlack | |
| Department of Mathematical
Sciences Lee University Cleveland, TN United States |
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| © 2023 MSP (Mathematical Sciences Publishers). |
