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arXiv:1011.0700 [math.DS]AbstractReferencesReviewsResources

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

W. Patrick Hooper

Published 2010-11-02, updated 2012-08-31Version 2

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.

Comments: 23 pages, 10 figures. Improved exposition. Theorem 10 is an improved geodesic coding result. arXiv admin note: text overlap with arXiv:0802.0189
Categories: math.DS
Subjects: 37D40, 37E99
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