Inventiones mathematicae

, Volume 215, Issue 3, pp 741–778 | Cite as

Classification of Rauzy–Veech groups: proof of the Zorich conjecture

  • Rodolfo Gutiérrez-RomoEmail author


We classify the Rauzy–Veech groups of all connected components of all strata of the moduli space of translation surfaces in absolute homology, showing, in particular, that they are commensurable to arithmetic lattices of symplectic groups. As a corollary, we prove a conjecture of Zorich about the Zariski-density of such groups.



I am grateful to Giovanni Forni for his interesting questions and remarks which motivated the newer versions of the article. I am also grateful to the two anonymous referees whose comments greatly improved the presentation of the results, and to my advisors, Anton Zorich and Carlos Matheus.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institut de Mathématiques de Jussieu – Paris Rive GaucheParis Cedex 13France

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