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

Abstract

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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.

How to cite

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Hubert, 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 -

References

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