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arXiv · 1011.0700

An Infinite Surface With The Lattice Property I: Veech Groups and Coding Geodesics

W. Patrick Hooper
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Abstract

We study the symmetries and geodesics of an infinite translation surface which arises as a limit of translation surfaces built from regular polygons, studied by Veech. We find the affine symmetry group of this infinite translation surface, and we show that this surface admits a deformation into other surfaces with topologically equivalent affine symmetries. The geodesics on these new surfaces are combinatorially the same as the geodesics on the original.

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W. Patrick Hooper. 2010-11-02. An Infinite Surface With The Lattice Property I: Veech Groups and Coding Geodesics. https://arxiv.org/abs/1011.0700

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