An Infinite Surface With The Lattice Property I: Veech Groups and Coding Geodesics
Dynamical Systems
2012-09-04 v2
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.
Cite
@article{arxiv.1011.0700,
title = {An Infinite Surface With The Lattice Property I: Veech Groups and Coding Geodesics},
author = {W. Patrick Hooper},
journal= {arXiv preprint arXiv:1011.0700},
year = {2012}
}
Comments
23 pages, 10 figures. Improved exposition. Theorem 10 is an improved geodesic coding result. arXiv admin note: text overlap with arXiv:0802.0189