Zorich conjecture for hyperelliptic Rauzy-Veech groups

TL;DR

This paper investigates the structure of hyperelliptic Rauzy diagrams and groups, providing a solution to Zorich's conjecture regarding the Zariski closure of Rauzy-Veech groups in hyperelliptic cases.

Contribution

It offers a detailed description of hyperelliptic Rauzy diagrams and groups, resolving the hyperelliptic cases of Zorich's conjecture on Zariski closures.

Findings

Structure of hyperelliptic Rauzy diagrams elucidated

Hyperelliptic Rauzy-Veech groups characterized

Solution to Zorich's hyperelliptic conjecture provided

Abstract

We describe the structure of hyperelliptic Rauzy diagrams and hyperelliptic Rauzy-Veech groups. In particular, this provides a solution of the hyperelliptic cases of a conjecture of Zorich on the Zariski closure of Rauzy-Veech groups.