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Connected components of the strata of the moduli spaces of quadratic differentials

Erwan Lanneau — 2008

Annales scientifiques de l'École Normale Supérieure

In two fundamental classical papers, Masur [14] and Veech [21] have independently proved that the Teichmüller geodesic flow acts ergodically on each connected component of each stratum of the moduli space of quadratic differentials. It is therefore interesting to have a classification of the ergodic components. Veech has proved that these strata are not necessarily connected. In a recent work [8], Kontsevich and Zorich have completely classified the components in the particular case where the quadratic...

On the minimum dilatation of pseudo-Anosov homeromorphisms on surfaces of small genus

Erwan LanneauJean-Luc Thiffeault — 2011

Annales de l’institut Fourier

We find the minimum dilatation of pseudo-Anosov homeomorphisms that stabilize an orientable foliation on surfaces of genus three, four, or five, and provide a lower bound for genus six to eight. Our technique also simplifies Cho and Ham’s proof of the least dilatation of pseudo-Anosov homeomorphisms on a genus two surface. For genus g = 2 to 5 , the minimum dilatation is the smallest Salem number for polynomials of degree 2 g .

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