#### Volume 20, issue 5 (2016)

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 The Journal About the Journal Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Subscriptions Author Index To Appear Contacts ISSN (electronic): 1364-0380 ISSN (print): 1465-3060
Rank two affine submanifolds in $\mathcal{H}(2,2)$ and $\mathcal{H}(3,1)$

### David Aulicino and Duc-Manh Nguyen

Geometry & Topology 20 (2016) 2837–2904
##### Abstract

We classify all rank two affine manifolds in strata in genus three with two zeros. This confirms a conjecture of Maryam Mirzakhani in these cases. Several technical results are proven for all strata in genus three, with the hope that they may shed light on a complete classification of rank two manifolds in genus three.

##### Keywords
translation surfaces, $\mathrm{GL}(2, \mathbb{R})$, orbit closure, moduli space of abelian differentials
Primary: 32G15
Secondary: 14H10