Cylinder deformations in orbit closures of translation surfaces

Wright, Alex¹

¹ Math Department, University of Chicago, 5734 South University Avenue 208C, Chicago, IL 60637, USA

Geometry & topology, Tome 19 (2015) no. 1, pp. 413-438.

Résumé

Let $M$ be a translation surface. We show that certain deformations of $M$ supported on the set of all cylinders in a given direction remain in the ${GL}^{+}\left(2,ℝ\right)$–orbit closure of $M$. Applications are given concerning complete periodicity, affine field of definition and the number of parallel cylinders which may be found on a translation surface in a given orbit closure.

Détail

DOI : 10.2140/gt.2015.19.413

Classification : 32G15, 37D40
Keywords: Teichmüller dynamics, translation surface

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