#### Volume 19, issue 1 (2015)

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Cylinder deformations in orbit closures of translation surfaces

### Alex Wright

Geometry & Topology 19 (2015) 413–438
##### Abstract

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.

##### Keywords
Teichmüller dynamics, translation surface
##### Mathematical Subject Classification 2010
Primary: 32G15, 37D40