2014/06/02 by Diego De Filippi, De Filippi, Diego
Engineering · Mathematics · #Advanced Combinatorial Mathematics #Advanced Materials and Mechanics #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric and Algebraic Topology #math.AG
paper · pdf · doi:10.48550/arxiv.1406.0366
arxiv created 2014/06/02 · openalex publication_date 2014/06/02 · arxiv updated 2014/06/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Take a Teichmüller disc whose corresponding flat surface has a Veech-Group that contains a parabolic element. We look at its image in Schottkyspace and show that we can always construct a Schottky covering such that this image is not a disc, and, in the case of translation surfaces, even a punctured disc. Firstly, we prove this for origamis (= square tiled closed translation surfaces) and, then, generalise the results to flat (resp. translation) surfaces. We also give an algorithm to find the corresponding subgroup of the fundamental group of the origami, and we give some examples. Moreover, we include an introduction to Teichmüller discs and Schottky space for the convenience of the reader.