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Veech Groups of Loch Ness Monsters

Piotr Przytycki, Gabriela Schmithüsen, Ferrán Valdez (2011)

Annales de l’institut Fourier

We classify Veech groups of tame non-compact flat surfaces. In particular we prove that all countable subgroups of G L + ( 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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