[Homologie des origamis avec symétries]
Étant donné un origami (surface à petits carreaux) avec un groupe d’automorphismes , nous déterminons la décomposition du premier groupe d’homologie de en -submodules isotypiques. Parmi l’action du groupe affine de sur le groupe d’homologie, nous déduisons quelques conséquences pour les multiplicités des exposants de Lyapunov du cocycle de Kontsevich-Zorich. De plus, nous construisons et étudions plusieurs familles d’origamis intéressants pour illustrer nos résultats.
Given an origami (square-tiled surface) with automorphism group , we compute the decomposition of the first homology group of into isotypic -submodules. Through the action of the affine group of 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.
Keywords: Origamis, square-tiled surfaces, automorphisms group, affine group, representations of finite groups, regular and quasi-regular origamis, Kontsevich-Zorich cocycle, Lyapunov exponents
Mot clés : origamis, surfaces à petits carreaux, groupes d’automorphismes, groupes affines, représentations des groupes finis, origamis réguliers et quasi-réguliers, cocycle de Kontsevich-Zorich, exposants de Lyapunov
Matheus, Carlos 1 ; Yoccoz, Jean-Christophe 2 ; Zmiaikou, David 3
@article{AIF_2014__64_3_1131_0,
author = {Matheus, Carlos and Yoccoz, Jean-Christophe and Zmiaikou, David},
title = {Homology of origamis with symmetries},
journal = {Annales de l'Institut Fourier},
pages = {1131--1176},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {64},
number = {3},
year = {2014},
doi = {10.5802/aif.2876},
mrnumber = {3330166},
zbl = {06387303},
language = {en},
url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2876/}
}
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 SP - 1131 EP - 1176 VL - 64 IS - 3 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2876/ DO - 10.5802/aif.2876 LA - en ID - AIF_2014__64_3_1131_0 ER -
%0 Journal Article %A Matheus, Carlos %A Yoccoz, Jean-Christophe %A Zmiaikou, David %T Homology of origamis with symmetries %J Annales de l'Institut Fourier %D 2014 %P 1131-1176 %V 64 %N 3 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.2876/ %R 10.5802/aif.2876 %G en %F AIF_2014__64_3_1131_0
Matheus, Carlos; Yoccoz, Jean-Christophe; Zmiaikou, David. Homology of origamis with symmetries. Annales de l'Institut Fourier, Tome 64 (2014) no. 3, pp. 1131-1176. doi : 10.5802/aif.2876. https://aif.centre-mersenne.org/articles/10.5802/aif.2876/
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