Abstract
We prove the Zorich–Kontsevich conjecture that the non-trivial Lyapunov exponents of the Teichmüller ow 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 Zorich and Kontsevich, this implies the existence of the complete asymptotic Lagrangian flag describing the behavior in homology of the vertical foliation in a typical translation surface.
Funding Statement
Work carried out within the Brazil–France Agreement in Mathematics. Avila is a Clay Research Fellow. Viana is partially supported by Pronex and Faperj.
Citation
Artur Avila. Marcelo Viana. "Simplicity of Lyapunov spectra: proof of the Zorich-Kontsevich conjecture." Acta Math. 198 (1) 1 - 56, 2007. https://doi.org/10.1007/s11511-007-0012-1
Information
