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arXiv:1207.2423 [math.DS]AbstractReferencesReviewsResources

Homology of origamis with symmetries

Carlos Matheus, Jean-Christophe Yoccoz, David Zmiaikou

Published 2012-07-10, updated 2013-09-03Version 2

Given an origami (square-tiled surface) M with automorphism group G, we compute the decomposition of the first homology group of M into isotypic G-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.

Comments: 36 pages, no figures. Final version incorporating the referee's comments. To appear in Annales de l'Institut Fourier, Volume 64 (2014)
Categories: math.DS
Subjects: 37D40, 30F10, 30F60, 32G15, 20C05
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