# The Arnoux-Yoccoz Teichmüller disc

Erwan Lanneau, Pascal Hubert, Martin Möller

Number | 2 |
---|---|

Author | Martin Möller |

Year | 2007 |

We prove that the Teichmüller disc stabilized by the Arnoux-Yoccoz
pseudo-Anosov possesses two transverse hyperbolic directions. This
proves that the corresponding flat surface has not a cyclic Veech group.
In addition, we prove that this Teichmüller disc is dense inside the
hyperelliptic locus of the connected component H^{odd}(2; 2).

We rephrase our results in terms of quadratic differentials: We show that there exists a holomorphic quadratic differential, on a genus 2 surface, with the two following properties.

(1) The Teichmüller disc is dense inside the moduli space of holomorphic quadratic differentials (which are not the global square of any Abelian differentials).

(2) The stabilizer of the PSL_{2}(R)-action contains two non commuting pseudo-Anosov diffeomorphisms.