Rank 2 Affine Manifolds in Genus 3

TL;DR

This paper fully classifies rank two affine manifolds within the moduli space of genus three translation surfaces, advancing the understanding of higher rank affine structures in this context.

Contribution

It completes the classification of rank two affine manifolds in genus three, building on recent results to finalize the higher rank classification.

Findings

Complete classification of rank two affine manifolds in genus three

Integration of recent Mirzakhani and Wright results

Advancement in understanding higher rank affine structures

Abstract

We complete the classification of rank two affine manifolds in the moduli space of translation surfaces in genus three. Combined with a recent result of Mirzakhani and Wright, this completes the classification of higher rank affine manifolds in genus three.