An algorithm for finding the Veech group of an origami

2004/01/15 by Gabriela Schmithuesen, Schmithuesen, Gabriela
Computer Science · Engineering · Mathematics · #14H10 #14H30 #53C10 #Advanced Graph Theory Research #Advanced Materials and Mechanics #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #math.AG #math.GT #msc:14H10 #msc:14H30 #msc:53C10

paper · pdf · doi:10.48550/arxiv.math/0401185

17 pages, 1 figure

arxiv created 2004/01/15 · openalex publication_date 2004/01/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the Veech group of an origami, i.e. of a translation surface, tessellated by parallelograms. We show that it is isomorphic to the image of a certain subgroup of Aut(F₂) in SL₂(Z) = Out⁺(F₂). Based on this we present an algorithm that determines the Veech group.

Related

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• Calculation of Veech groups and Galois invariants of general origamis
• General origamis and Veech groups of flat surfaces
• Totally non congruence Veech groups
• Regular origamis with totally non-congruence groups as Veech groups