Veech groups of Loch Ness monsters

Abstract

We classify Veech groups of tame non-compact flat surfaces. In particular we prove that all countable subgroups of ${\mathbf{GL}}_{+}(2,\mathbb{R})$ 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.

15 pages

References in corpus (3)

• Dynamics on an infinite surface with the lattice property
• Veech groups, irrational billiards and stable abelian differentials
• Characterizations of lattice surfaces

Cited by in corpus (5)

• Isometry groups of infinite-genus hyperbolic surfaces
• Fibered 3-manifolds and Veech groups
• On the Ends of groups and the Veech groups of infinite-genus surfaces
• Geometric Schotkky groups and non compact hyperbolic surface with infinite genus
• Wild singularities of flat surfaces