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Homology of origamis with symmetries

Carlos Matheus; Jean-Christophe Yoccoz; David Zmiaikou — 2014

Annales de l’institut Fourier

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.

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