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arXiv · 1605.05659

Cutting sequences on square-tiled surfaces

Charles C. Johnson
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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.

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Charles C. Johnson. 2016-05-17. Cutting sequences on square-tiled surfaces. https://doi.org/10.1007/s10711-017-0227-z

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