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

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.

arXiv comment23 pages, 10 figures. Improved exposition. Theorem 10 is an improved geodesic coding result. arXiv admin note: text overlap with arXiv:0802.0189