Dynamics in the moduli space of Abelian differentials (Q815190)

The authors announce the proof of the Zorich-Kontsevich conjecture: the nontrivial Lyapunov exponents of the Teichmüller flow on (any connected component of a stratum of) the moduli space of abelian differentials on compact Riemann surfaces are all distinct. By previous work of those authors, this implies the existence of the complete asymptotic Lagrangian flag describing the behavior in homology of the vertical foliation in a typical translation surface. The authors' proof of the Zorich-Kontsevich conjecture has two distinct parts: 1) a general criterion for the simplicity of the Lyapunov spectrum of locally constant cocycles; 2) a combinatorial analysis of Rauzy diagrams to show that the criterion can be applied to the Zorich cocycle on any Rauzy class.