Canonical translation surfaces for computing Veech groups

DOI10.1007/s10711-022-00723-5OpenAlexW3195216044MaRDI QIDQ2168039

Thomas A. Schmidt, Brandon Edwards, Slade Sanderson

Publication date: 31 August 2022

Published in: Geometriae Dedicata (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2012.12444

zbMATH Keywords

Fuchsian grouptranslation surfaceDirichlet domainVeech group

Mathematics Subject Classification ID

Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) (32G15) Fuchsian groups and their generalizations (group-theoretic aspects) (20H10) Teichmüller theory for Riemann surfaces (30F60) Tilings in (2) dimensions (aspects of discrete geometry) (52C20) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40) Fuchsian and Kleinian groups as dynamical systems (37F32)

Related Items (1)

Constructing lattice surfaces with prescribed Veech groups: an algorithm

Uses Software

• SageMath
• GitHub

Cites Work

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• Fundamental domains and generators for lattice Veech groups
• Characterizations of lattice surfaces
• Teichmüller curves, triangle groups, and Lyapunov exponents
• Teichmüller curves in moduli space, Eisenstein series and an application to triangular billiards
• Hausdorff dimension of sets of nonergodic measured foliations
• Connected components of the moduli spaces of Abelian differentials with prescribed singularities
• Billiards on rational-angled triangles
• Teichmüller geodesics of infinite complexity.
• Translation surfaces and their orbit closures: an introduction for a broad audience
• Ellipses in translation surfaces
• Bicuspid F -structures and Hecke groups
• An Algorithm for Finding the Veech Group of an Origami
• On triangular billiards

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