English

Veech groups of Loch Ness monsters

Differential Geometry 2017-02-08 v1 Group Theory

Abstract

We classify Veech groups of tame non-compact flat surfaces. In particular we prove that all countable subgroups of GL+(2,R)\mathbf{GL}_+(2,\R) avoiding the set of mappings of norm less than 1 appear as Veech groups of tame non-compact flat surfaces which are Loch Ness monsters. Conversely, a Veech group of any tame flat surface is either countable, or one of three specific types.

Cite

@article{arxiv.0906.5268,
  title  = {Veech groups of Loch Ness monsters},
  author = {Piotr Przytycki and Gabriela Schmithuesen and Ferran Valdez},
  journal= {arXiv preprint arXiv:0906.5268},
  year   = {2017}
}

Comments

15 pages

R2 v1 2026-06-21T13:18:56.171Z