Rank two affine submanifolds in ℋ(2,2) and ℋ(3,1)

Aulicino, David¹ ; Nguyen, Duc-Manh²

¹ Department of Mathematics, University of Chicago, 5734 University Avenue, Chicago, IL 60637, United States
² University of Bordeaux, Bat. A33, IMB, CNRS UMR 5251, 351, cours de la Libération, F-33405 Talence, France

Geometry & topology, Tome 20 (2016) no. 5, pp. 2837-2904.

Résumé

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.

Détail

DOI : 10.2140/gt.2016.20.2837

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

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