An infinite surface with the lattice property I: Veech groups and coding geodesics

Hooper, W.

doi:10.1090/S0002-9947-2013-06139-9

An infinite surface with the lattice property I: Veech groups and coding geodesics
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Trans. Amer. Math. Soc. 366 (2014), 2625-2649 Request permission

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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