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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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