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Simplicity of Lyapunov spectra: proof of the Zorich-Kontsevich conjecture

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Acta Mathematica

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.

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Authors and Affiliations

  1. CNRS UMR 7599, Laboratoire de Probabilités et Modèles Aléatoires, Université Pierre et Marie Curie, Boîte Postale 188, FR-75252, Paris Cedex 05, France

    Artur Avila

  2. IMPA – Instituto Nacional de Matemática Pura e Aplicada, Estrada Dona Castorina 110, 22460-320, Rio de Janeiro, Brazil

    Marcelo Viana

Authors
  1. Artur Avila
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  2. Marcelo Viana
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Correspondence to Artur Avila.

Additional information

Work carried out within the Brazil–France Agreement in Mathematics. Avila is a Clay Research Fellow. Viana is partially supported by Pronex and Faperj.

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Avila, A., Viana, M. Simplicity of Lyapunov spectra: proof of the Zorich-Kontsevich conjecture. Acta Math 198, 1–56 (2007). https://doi.org/10.1007/s11511-007-0012-1

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  • DOI: https://doi.org/10.1007/s11511-007-0012-1

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