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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

   

 

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


Author: W. Patrick Hooper
Journal: Trans. Amer. Math. Soc. 366 (2014), 2625-2649
MSC (2010): Primary 37D40, 37D50, 37E99, 32G15
Published electronically: December 11, 2013
MathSciNet review: 3165649
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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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Additional Information

W. Patrick Hooper
Affiliation: Department of Mathematics, City College of New York, New York, New York 10031
Email: whooper@ccny.cuny.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-2013-06139-9
Received by editor(s): November 3, 2010
Received by editor(s) in revised form: September 5, 2012
Published electronically: December 11, 2013
Additional Notes: This research was supported by N.S.F. Postdoctoral Fellowship DMS-0803013, N.S.F. Grant DMS-1101233, and a PSC-CUNY Award (funded by The Professional Staff Congress and The City University of New York).
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.