# Veech Groups of Loch Ness Monsters

Piotr Przytycki^{[1]}; Gabriela Schmithüsen^{[2]}; Ferrán Valdez^{[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)

Annales de l’institut Fourier (2011)

- Volume: 61, Issue: 2, page 673-687
- ISSN: 0373-0956

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top## How to cite

topPrzytycki, Piotr, Schmithüsen, Gabriela, and Valdez, Ferrán. "Veech Groups of Loch Ness Monsters." Annales de l’institut Fourier 61.2 (2011): 673-687. <http://eudml.org/doc/219716>.

@article{Przytycki2011,

abstract = {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.},

affiliation = {Polish Academy of Sciences Institute of Mathematics Śniadeckich 8 00-956 Warsaw (Poland); Karlsruhe Institute of Technology Institute of Algebra and Geometry 76128 Karlsruhe (Germany); U.N.A.M. Campus Morelia Morelia, Michoacán (Mexico)},

author = {Przytycki, Piotr, Schmithüsen, Gabriela, Valdez, Ferrán},

journal = {Annales de l’institut Fourier},

keywords = {Translation surfaces; infinite genus surfaces; Veech groups; translation surfaces},

language = {eng},

number = {2},

pages = {673-687},

publisher = {Association des Annales de l’institut Fourier},

title = {Veech Groups of Loch Ness Monsters},

url = {http://eudml.org/doc/219716},

volume = {61},

year = {2011},

}

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

PB - Association des Annales de l’institut Fourier

VL - 61

IS - 2

SP - 673

EP - 687

AB - 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.

LA - eng

KW - Translation surfaces; infinite genus surfaces; Veech groups; translation surfaces

UR - http://eudml.org/doc/219716

ER -

## References

top- Étienne Ghys, Topologie des feuilles génériques, Ann. of Math. (2) 141 (1995), 387-422 Zbl0843.57026MR1324140
- P. Hooper, Dynamics on an infinite surface with the lattice property, (2008)
- P. Hoopert, P. Hubert, B Weiss, Dynamics on the infinite staircase surface, (2008)
- P. Hubert, G. Schmithüsen, Infinite translation surfaces with infinitely generated Veech groups, (2008) Zbl1219.30019MR2753950
- Pascal Hubert, Howard Masur, Thomas Schmidt, Anton Zorich, Problems on billiards, flat surfaces and translation surfaces, Problems on mapping class groups and related topics 74 (2006), 233-243, Amer. Math. Soc., Providence, RI Zbl1307.37019MR2264543
- Pascal Hubert, Thomas A. Schmidt, An introduction to Veech surfaces, Handbook of dynamical systems. Vol. 1B (2006), 501-526, Elsevier B. V., Amsterdam Zbl1130.37367MR2186246
- John Smillie, Barak Weiss, Characterizations of lattice surfaces, Invent. Math. 180 (2010), 535-557 Zbl1195.57041MR2609249
- J. F. Valdez, Infinite genus surfaces and irrational polygonal billiards, Geom. Dedicata 143 (2009), 143-154 Zbl1190.37040MR2576299
- J. F. Valdez, Veech groups, irrational billiards and stable abelian differentials, (2009) Zbl1260.37024
- W. A. Veech, Teichmüller curves in moduli space, Eisenstein series and an application to triangular billiards, Invent. Math. 97 (1989), 553-583 Zbl0676.32006MR1005006

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