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Topological Veech dichotomy and tessellations of the hyperbolic plane
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | NGUYEN, Duc-Manh | |
| dc.date.accessioned | 2024-04-04T03:04:11Z | |
| dc.date.available | 2024-04-04T03:04:11Z | |
| dc.date.issued | 2022-06 | |
| dc.identifier.issn | 0021-2172 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/193130 | |
| dc.description.abstractEn | 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. | |
| dc.language.iso | en | |
| dc.publisher | Springer | |
| dc.title.en | Topological Veech dichotomy and tessellations of the hyperbolic plane | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1007/s11856-022-2320-8 | |
| dc.subject.hal | Mathématiques [math]/Topologie géométrique [math.GT] | |
| dc.subject.hal | Mathématiques [math]/Théorie des groupes [math.GR] | |
| dc.identifier.arxiv | 1808.09329 | |
| bordeaux.journal | Israel Journal of Mathematics | |
| bordeaux.page | 577-616 | |
| bordeaux.volume | 249 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 2 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01925664 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01925664v1 | |
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