Veech Groups and Translation Coverings
Abstract:
A translation surface is obtained by taking plane polygons and gluing their edges by translations.
We ask which subgroups of the Veech group of a primitive translation surface can be realised via a translation covering.
For many primitive surfaces we prove that partition stabilising congruence subgroups are the Veech group of a covering surface.
We also address the coverings via their monodromy groups and present examples of cyclic coverings in short orbits, i.e. with large Veech groups.
We ask which subgroups of the Veech group of a primitive translation surface can be realised via a translation covering.
For many primitive surfaces we prove that partition stabilising congruence subgroups are the Veech group of a covering surface.
We also address the coverings via their monodromy groups and present examples of cyclic coverings in short orbits, i.e. with large Veech groups.
| Zugehörige Institution(en) am KIT | Institut für Algebra und Geometrie (IAG) |
| Publikationstyp | Hochschulschrift |
| Publikationsjahr | 2013 |
| Sprache | Englisch |
| Identifikator | urn:nbn:de:swb:90-363659 KITopen-ID: 1000036365 |
| Verlag | Karlsruher Institut für Technologie (KIT) |
| Art der Arbeit | Dissertation |
| Fakultät | Fakultät für Mathematik (MATH) |
| Institut | Institut für Algebra und Geometrie (IAG) |
| Prüfungsdaten | 10.07.2013 |
| Schlagwörter | Veech group, congruence subgroup, monodromy group, cyclic covering, regular polygons, translation covering |
| Relationen in KITopen | |
| Referent/Betreuer | Weitze-Schmithüsen, J. Prof. G. |