Posted by: **matheuscmss** | December 9, 2009

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

Today Jean-Christophe Yoccoz and I uploaded to the arXiv our joint paper “*The action of the affine diffeomorphisms on the relative homology group of certain exceptionally symmetric origamis*“. Since the goal of this paper was already explained in this previous post (where the reader can also find some slides of a talk I gave at Orsay a few months ago), here I will only reproduce the abstract of the paper:

*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 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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Posted in math.DS, Mathematics, papers | Tags: Action on relative homology, Affine diffeomorphisms, D_4 root systems, Eierlegende Wollmilchsau, Kontsevich-Zorich cocycle, Origamis, SL(2;R)-action on Abelian differentials, Teichmüller curves, Teichmüller flow, Veech group, Veech surfaces

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