Topological Veech dichotomy and tessellations of the hyperbolic plane
Langue
en
Article de revue
Ce document a été publié dans
Israel Journal of Mathematics. 2022-06, vol. 249, n° 2, p. 577-616
Springer
Résumé en anglais
We construct for every half-translation surface a tessellation of the Poincare upper half plane generalising the Farey tessellation for a flat torus. By construction, the Veech group stabilizes this tessellation. As a ...Lire la suite >
We construct for every half-translation surface a tessellation of the Poincare upper half plane generalising the Farey tessellation for a flat torus. By construction, the Veech group stabilizes this tessellation. As a consequence, we get a bound on the volume of the corresponding Teichm\"uller curve for a lattice surface (Veech surface). There is a natural graph underlying this tessellation on which the affine group acts by automorphisms. We provide algorithms to determine a `coarse' fundamental domain and a generating set for the Veech group based on this graph. We also show that this graph has infinite diameter and is Gromov hyperbolic.< Réduire
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