Veech groups of Loch Ness monsters

Details Veech groups of Loch Ness monsters Veech groups of Loch Ness monsters

2009-06-29

arxiv.org/abs/0906.5268v1

Mathematics

Differential Geometry

15 pages

Scientific paper

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

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