Invariants of translation surfaces

DOI10.5802/aif.1829zbMath0985.32008OpenAlexW1576195261MaRDI QIDQ5928784

Pascal Hubert, Thomas A. Schmidt

Publication date: 4 April 2001

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIF_2001__51_2_461_0

zbMATH Keywords

billiardsaffine coveringsflat surfacesHecke triangle groupsTeichmüller diskstree of balancedVeech groups

Mathematics Subject Classification ID

Groups acting on specific manifolds (57S25) Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) (32G15) Teichmüller theory for Riemann surfaces (30F60) Geometric structures on manifolds of high or arbitrary dimension (57N16)

Related Items

Infinitely generated Veech groups, Schwarz triangle mappings and Teichmüller curves: The Veech-Ward-Bouw-Möller curves, Congruence Veech groups, Prime arithmetic Teichmüller discs in \({\mathcal H}(2)\), On the areas of the minimal triangles in Veech surfaces, Topological Veech dichotomy and tessellations of the hyperbolic plane, Infinitely many lattice surfaces with special pseudo-Anosov maps, Translation covers among triangular billiard surfaces, Slope gap distribution of saddle connections on the \(2n\)-gon, Moduli spaces of Abelian differentials: the principal boundary, counting problems, and the Siegel-Veech constants, An Algorithm for Finding the Veech Group of an Origami, On Minkowski constants of Veech surfaces, Cylinder deformations in orbit closures of translation surfaces, A series of coverings of the regular \(n\)-gon, Teichmüller curves, triangle groups, and Lyapunov exponents, Periodic points on Veech surfaces and the Mordell-Weil group over a Teichmüller curve, An extraordinary origami curve, The conformal geometry of billiards, Teichmüller curves, Galois actions and $ \widehat {GT} $‐relations, Geometry of infinitely generated Veech groups, Affine diffeomorphisms of translation surfaces: Periodic points, Fuchsian groups, and arithmeticity, Hodge-Teichmüller planes and finiteness results for Teichmüller curves, Platonic Solids and High Genus Covers of Lattice Surfaces

Cites Work

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• Les surfaces euclidiennes à singularités coniques. (Euclidean surfaces with cone singularities)
• Ergodicity of billiard flows and quadratic differentials
• Teichmüller curves in moduli space, Eisenstein series and an application to triangular billiards
• The Caratheodory metric on abelian Teichmüller disks
• The billiard in a regular polygon
• Über die Heckeschen Gruppen \(G(\lambda)\). II
• Topological transitivity of billiards in polygons
• Period matrices of hyperelliptic curves
• An extension of Lagrange's theorem to interval exchange transformations over quadratic fields
• Billiards on rational-angled triangles
• Affine mappings of translation surfaces: Geometry and arithmetic
• Veech groups and polygonal coverings
• Continued fractions on the Veech surfaces
• The geometry and arithmetic of translation surfaces with applications to polygonal billiards
• Closed trajectories for quadratic differentials with an application to billiards
• Bestimmung der Kommensurabilitätsklasse der Hilbertschen Modulgruppe
• Some compact invariant sets for hyperbolic linear automorphisms of torii
• Calculation of Fuchsian groups associated to billiards in a rational triangle
• Planar structures and billiards in rational polygons: the Veech alternative