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

## TL;DR

This paper classifies Rauzy-Veech groups across all strata of translation surfaces, proving they are related to arithmetic lattices and confirming Zorich's conjecture on their Zariski-density.

## Contribution

It provides a complete classification of Rauzy-Veech groups and proves the Zorich conjecture on their Zariski-density in the context of translation surfaces.

## Key findings

- Rauzy-Veech groups are commensurable to arithmetic lattices of symplectic groups
- Confirmed Zorich's conjecture on Zariski-density of these groups
- Classification applies to all connected components of all strata

## 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.