Cutting sequences on square-tiled surfaces
Dynamical Systems
2017-02-06 v3 Metric Geometry
Abstract
We characterize cutting sequences of infinite geodesics on square-tiled surfaces by considering interval exchanges on specially chosen intervals on the surface. These interval exchanges can be thought of as skew products over a rotation, and we convert cutting sequences to symbolic trajectories of these interval exchanges to show that special types of combinatorial lifts of Sturmian sequences completely describe all cutting sequences on a square-tiled surface. Our results extend the list of families of surfaces where cutting sequences are understood to a dense subset of the moduli space of all translation surfaces.
Cite
@article{arxiv.1605.05659,
title = {Cutting sequences on square-tiled surfaces},
author = {Charles C. Johnson},
journal= {arXiv preprint arXiv:1605.05659},
year = {2017}
}
Comments
28 pages, 12 figures. Minor revisions and corrections. To appear in Geometriae Dedicata