Homology of origamis with symmetries
[Homologie des origamis avec symétries]
Matheus, Carlos ; Yoccoz, Jean-Christophe ; Zmiaikou, David
Annales de l'Institut Fourier, Tome 64 (2014), p. 1131-1176 / Harvested from Numdam
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Étant donné un origami (surface à petits carreaux) M avec un groupe d’automorphismes Γ, nous déterminons la décomposition du premier groupe d’homologie de M en Γ-submodules isotypiques. Parmi l’action du groupe affine de M 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) 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.

Publié le : 2014-01-01
DOI : https://doi.org/10.5802/aif.2876
Classification:  37D40,  30F10,  32G15,  20C05
Mots 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 
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     author = {Matheus, Carlos and Yoccoz, Jean-Christophe and Zmiaikou, David},
     title = {Homology of origamis with symmetries},
     journal = {Annales de l'Institut Fourier},
     volume = {64},
     year = {2014},
     pages = {1131-1176},
     doi = {10.5802/aif.2876},
     zbl = {06387303},
     mrnumber = {3330166},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_2014__64_3_1131_0}
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Matheus, Carlos; Yoccoz, Jean-Christophe; Zmiaikou, David. Homology of origamis with symmetries. Annales de l'Institut Fourier, Tome 64 (2014) pp. 1131-1176. doi : 10.5802/aif.2876. http://gdmltest.u-ga.fr/item/AIF_2014__64_3_1131_0/

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