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arXiv · 0912.1425

The action of the affine diffeomorphisms on the relative homology group of certain exceptionally symmetric origamis

Carlos Matheus·Jean-Christophe Yoccoz
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Abstract

We compute explicitly the action of the group of affine diffeomorphisms on the relative homology of two remarkable origamis discovered respectively by Forni (in genus 3) and Forni-Matheus (in genus 4). We show that, in both cases, the action on the non trivial part of the homology is through finite groups. In particular, the action on some 4-dimensional invariant subspace of the homology leaves invariant a root system of $D_4$ type. This provides as a by-product a new proof of (slightly stronger versions of) the results of Forni and Matheus: the non trivial Lyapunov exponents of the Kontsevich-Zorich cocycle for the Teichmuller disks of these two origamis are equal to zero.

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Carlos Matheus, Jean-Christophe Yoccoz. 2010-10-06. The action of the affine diffeomorphisms on the relative homology group of certain exceptionally symmetric origamis. https://arxiv.org/abs/0912.1425

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