Dynamics in the moduli space of Abelian differentials
type: Item
instance of: scholarly article
title: Dynamics in the moduli space of Abelian differentials
zbMATH Open document ID: 1087.14014
author: Artur Avila
author: Marcelo Viana
published in: Portugaliae Mathematica. Nova Série
publication date: 2006-02-22T00:00:00Z
full work available at URL: https://eudml.org/doc/52333
review text: 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.
reviewed by: V. V. Chueshev
Mathematics Subject Classification ID: 14F10
Mathematics Subject Classification ID: 14F05
Mathematics Subject Classification ID: 14H15
Mathematics Subject Classification ID: 14H60
Mathematics Subject Classification ID: 32G15
Mathematics Subject Classification ID: 37D40
zbMATH DE Number: 5008900
zbMATH Keywords: Zorich-Kontsevich conjecture
zbMATH Keywords: Lyapunov exponents of the Teichüeller flow on the moduli space
zbMATH Keywords: compact Riemann surface
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5008900