Veech Groups of Loch Ness Monsters
Annales de l'Institut Fourier, Volume 61 (2011) no. 2, p. 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 : https://doi.org/10.5802/aif.2625
Classification:  20F65,  53A99
Keywords: Translation surfaces, infinite genus surfaces, Veech groups
@article{AIF_2011__61_2_673_0,
     author = {Przytycki, Piotr and Schmith\"usen, Gabriela and Valdez, Ferr\'an},
     title = {Veech Groups of Loch Ness Monsters},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {61},
     number = {2},
     year = {2011},
     pages = {673-687},
     doi = {10.5802/aif.2625},
     zbl = {1266.32016},
     mrnumber = {2895069},
     language = {en},
     url = {https://aif.centre-mersenne.org/item/AIF_2011__61_2_673_0}
}
Veech Groups of Loch Ness Monsters. Annales de l'Institut Fourier, Volume 61 (2011) no. 2, pp. 673-687. doi : 10.5802/aif.2625. https://aif.centre-mersenne.org/item/AIF_2011__61_2_673_0/

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