Cylinder deformations in orbit closures of translation surfaces

Wright, Alex

doi:10.2140/gt.2015.19.413

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Cylinder deformations in orbit closures of translation surfaces

Alex Wright

Geometry & Topology 19 (2015) 413–438

DOI: 10.2140/gt.2015.19.413

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 ${GL}^{+} (2, ℝ)$ –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

References

Publication

Received: 11 October 2013

Accepted: 1 July 2014

Published: 27 February 2015

Proposed: Danny Calegari

Seconded: Benson Farb, Leonid Polterovich

Authors

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

Volume 19, issue 1 (2015)