# Invariants of translation surfaces

Pascal Hubert^{[1]}; Thomas A. Schmidt^{[2]}

- [1] Institut de Mathématiques de Luminy, Case 907, 163 avenue de Luminy, 13288 Marseille Cedex 09 (France)
- [2] Oregon State University, Department of Mathematics, Kidder Hall 368, Corvallis OR 97331-4605 (USA)

Annales de l’institut Fourier (2001)

- Volume: 51, Issue: 2, page 461-495
- ISSN: 0373-0956

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topHubert, Pascal, and Schmidt, Thomas A.. "Invariants of translation surfaces." Annales de l’institut Fourier 51.2 (2001): 461-495. <http://eudml.org/doc/115922>.

@article{Hubert2001,

abstract = {We definite invariants of translation surfaces which refine Veech groups. These aid in
exact determination of Veech groups. We give examples where two surfaces of isomorphic
Veech group cannot even share a common tree of balanced affine coverings. We also show
that there exist translation surfaces of isomorphic Veech groups which cannot affinely
cover any common surface. We also extend a result of Gutkin and Judge and thereby give
the first examples of noncompact Fuchsian groups which cannot appear as Veech groups. We
give an infinite family of these.},

affiliation = {Institut de Mathématiques de Luminy, Case 907, 163 avenue de Luminy, 13288 Marseille Cedex 09 (France); Oregon State University, Department of Mathematics, Kidder Hall 368, Corvallis OR 97331-4605 (USA)},

author = {Hubert, Pascal, Schmidt, Thomas A.},

journal = {Annales de l’institut Fourier},

keywords = {flat surfaces; Teichmüller disks; billiards; Hecke triangle groups; Veech groups; tree of balanced; affine coverings},

language = {eng},

number = {2},

pages = {461-495},

publisher = {Association des Annales de l'Institut Fourier},

title = {Invariants of translation surfaces},

url = {http://eudml.org/doc/115922},

volume = {51},

year = {2001},

}

TY - JOUR

AU - Hubert, Pascal

AU - Schmidt, Thomas A.

TI - Invariants of translation surfaces

JO - Annales de l’institut Fourier

PY - 2001

PB - Association des Annales de l'Institut Fourier

VL - 51

IS - 2

SP - 461

EP - 495

AB - We definite invariants of translation surfaces which refine Veech groups. These aid in
exact determination of Veech groups. We give examples where two surfaces of isomorphic
Veech group cannot even share a common tree of balanced affine coverings. We also show
that there exist translation surfaces of isomorphic Veech groups which cannot affinely
cover any common surface. We also extend a result of Gutkin and Judge and thereby give
the first examples of noncompact Fuchsian groups which cannot appear as Veech groups. We
give an infinite family of these.

LA - eng

KW - flat surfaces; Teichmüller disks; billiards; Hecke triangle groups; Veech groups; tree of balanced; affine coverings

UR - http://eudml.org/doc/115922

ER -

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## Citations in EuDML Documents

top- Eugene Gutkin, Pascal Hubert, Thomas A. Schmidt, Affine diffeomorphisms of translation surfaces : periodic points, fuchsian groups, and arithmeticity
- Alex Eskin, Howard Masur, Anton Zorich, Moduli spaces of abelian differentials : the principal boundary, counting problems, and the Siegel-Veech constants

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