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Carlos Matheus; Jean-Christophe Yoccoz; David Zmiaikou
Homology of origamis with symmetries
(Homologie des origamis avec symétries)
Annales de l'institut Fourier, 64 no. 3 (2014), p. 1131-1176, doi: 10.5802/aif.2876
Article PDF | Analyses MR 3330166 | Zbl 06387303
Voir aussi un erratum à cet article
Class. Math.: 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

Résumé - Abstract

Étant donné un origami (surface à petits carreaux) $M$ avec un groupe d’automorphismes $\Gamma $, nous déterminons la décomposition du premier groupe d’homologie de $M$ en $\Gamma $-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.

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