[Groupes de Veech du monstre du Loch Ness]
Nous classifions les groupes de Veech des surfaces de translation non compactes domestiquées. En particulier, nous prouvons que tous les sous groupes dénombrables de 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.
We classify Veech groups of tame non-compact flat surfaces. In particular we prove that all countable subgroups of ) 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.
Keywords: Translation surfaces, infinite genus surfaces, Veech groups
Mot clés : surfaces de translation, surfaces de genre infini, groupes de Veech
@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},
pages = {673--687},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {61},
number = {2},
year = {2011},
doi = {10.5802/aif.2625},
zbl = {1266.32016},
mrnumber = {2895069},
language = {en},
url = {http://archive.numdam.org/articles/10.5802/aif.2625/}
}
TY - JOUR AU - Przytycki, Piotr AU - Schmithüsen, Gabriela AU - Valdez, Ferrán TI - Veech Groups of Loch Ness Monsters JO - Annales de l'Institut Fourier PY - 2011 SP - 673 EP - 687 VL - 61 IS - 2 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.2625/ DO - 10.5802/aif.2625 LA - en ID - AIF_2011__61_2_673_0 ER -
%0 Journal Article %A Przytycki, Piotr %A Schmithüsen, Gabriela %A Valdez, Ferrán %T Veech Groups of Loch Ness Monsters %J Annales de l'Institut Fourier %D 2011 %P 673-687 %V 61 %N 2 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.2625/ %R 10.5802/aif.2625 %G en %F AIF_2011__61_2_673_0
Przytycki, Piotr; Schmithüsen, Gabriela; Valdez, Ferrán. Veech Groups of Loch Ness Monsters. Annales de l'Institut Fourier, Tome 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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