Volume 20, issue 5 (2016)

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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
Mathematical Subject Classification 2010
Primary: 32G15
Secondary: 14H10
References
Publication
Received: 15 March 2015
Revised: 28 July 2015
Accepted: 23 November 2015
Published: 7 October 2016
Proposed: Benson Farb
Seconded: Danny Calegari, Martin Bridson
Authors
David Aulicino
Department of Mathematics
University of Chicago
5734 University Avenue
Chicago, IL 60637
United States
Duc-Manh Nguyen
University of Bordeaux
Bat. A33
IMB, CNRS UMR 5251
351, cours de la Libération
F-33405 Talence
France