Veech Groups of Loch Ness Monsters
Annales de l'Institut Fourier, Volume 61 (2011) no. 2, pp. 673-687.

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

Nous classifions les groupes de Veech des surfaces de translation non compactes domestiquées. En particulier, nous prouvons que tous les sous groupes dénombrables de GL + (2,R) n’ayant pas d’éléments de norme plus petite que 1 apparaissent comme groupes de Veech des surfaces de translation non compactes domestiquées et dont le type topologique est celui du monstre du Loch Ness. Réciproquement, tout groupe de Veech d’une surface domestiquée est dénombrable ou bien conjugué à  un des trois groupes que nous précisons dans cet article.

DOI: 10.5802/aif.2625
Classification: 20F65,  53A99
Keywords: Translation surfaces, infinite genus surfaces, Veech groups
Przytycki, Piotr 1; Schmithüsen, Gabriela 2; Valdez, Ferrán 3

1 Polish Academy of Sciences Institute of Mathematics Śniadeckich 8 00-956 Warsaw (Poland)
2 Karlsruhe Institute of Technology Institute of Algebra and Geometry 76128 Karlsruhe (Germany)
3 U.N.A.M. Campus Morelia Morelia, Michoacán (Mexico)
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Przytycki, Piotr; Schmithüsen, Gabriela; Valdez, Ferrán. Veech Groups of Loch Ness Monsters. Annales de l'Institut Fourier, Volume 61 (2011) no. 2, pp. 673-687. doi : 10.5802/aif.2625. http://archive.numdam.org/articles/10.5802/aif.2625/

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