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

Abstract

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.

26 pages, no figures. This version includes minor corrections

References in corpus (2)

• Zero Lyapunov exponents and monodromy of the Kontsevich-Zorich cocycle
• Simplicity of the Lyapunov spectra of certain quadratic differentials

Cited by in corpus (3)

• Relative homological representations of framed mapping class groups
• On Selberg's Eigenvalue Conjecture for moduli spaces of abelian differentials
• Counting saddle connections in a homology class modulo $q$