Homology of origamis with symmetries

Carlos Matheus[1]; Jean-Christophe Yoccoz[2]; David Zmiaikou[3]

  • [1] Université Paris 13 Sorbonne Paris Cité LAGA, CNRS (UMR 7539) F-93430, Villetaneuse (France)
  • [2] Collège de France (PSL) 3, Rue d’Ulm 75005 Paris (France)
  • [3] Département de Mathématiques Université Paris-Sud 11 91405 Orsay Cedex (France)

Annales de l’institut Fourier (2014)

  • Volume: 64, Issue: 3, page 1131-1176
  • ISSN: 0373-0956

Abstract

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Given an origami (square-tiled surface) M with automorphism group Γ , we compute the decomposition of the first homology group of M into isotypic Γ -submodules. Through the action of the affine group of M on the homology group, we deduce some consequences for the multiplicities of the Lyapunov exponents of the Kontsevich-Zorich cocycle. We also construct and study several families of interesting origamis illustrating our results.

How to cite

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Matheus, Carlos, Yoccoz, Jean-Christophe, and Zmiaikou, David. "Homology of origamis with symmetries." Annales de l’institut Fourier 64.3 (2014): 1131-1176. <http://eudml.org/doc/275646>.

@article{Matheus2014,
abstract = {Given an origami (square-tiled surface) $M$ with automorphism group $\Gamma $, we compute the decomposition of the first homology group of $M$ into isotypic $\Gamma $-submodules. Through the action of the affine group of $M$ on the homology group, we deduce some consequences for the multiplicities of the Lyapunov exponents of the Kontsevich-Zorich cocycle. We also construct and study several families of interesting origamis illustrating our results.},
affiliation = {Université Paris 13 Sorbonne Paris Cité LAGA, CNRS (UMR 7539) F-93430, Villetaneuse (France); Collège de France (PSL) 3, Rue d’Ulm 75005 Paris (France); Département de Mathématiques Université Paris-Sud 11 91405 Orsay Cedex (France)},
author = {Matheus, Carlos, Yoccoz, Jean-Christophe, Zmiaikou, David},
journal = {Annales de l’institut Fourier},
keywords = {Origamis; square-tiled surfaces; automorphisms group; affine group; representations of finite groups; regular and quasi-regular origamis; Kontsevich-Zorich cocycle; Lyapunov exponents; origamis},
language = {eng},
number = {3},
pages = {1131-1176},
publisher = {Association des Annales de l’institut Fourier},
title = {Homology of origamis with symmetries},
url = {http://eudml.org/doc/275646},
volume = {64},
year = {2014},
}

TY - JOUR
AU - Matheus, Carlos
AU - Yoccoz, Jean-Christophe
AU - Zmiaikou, David
TI - Homology of origamis with symmetries
JO - Annales de l’institut Fourier
PY - 2014
PB - Association des Annales de l’institut Fourier
VL - 64
IS - 3
SP - 1131
EP - 1176
AB - Given an origami (square-tiled surface) $M$ with automorphism group $\Gamma $, we compute the decomposition of the first homology group of $M$ into isotypic $\Gamma $-submodules. Through the action of the affine group of $M$ on the homology group, we deduce some consequences for the multiplicities of the Lyapunov exponents of the Kontsevich-Zorich cocycle. We also construct and study several families of interesting origamis illustrating our results.
LA - eng
KW - Origamis; square-tiled surfaces; automorphisms group; affine group; representations of finite groups; regular and quasi-regular origamis; Kontsevich-Zorich cocycle; Lyapunov exponents; origamis
UR - http://eudml.org/doc/275646
ER -

References

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