Veech surfaces and simple closed curves

Max Forester; Robert Tang; Jing Tao

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arXiv · 1605.01772

Veech surfaces and simple closed curves

Max Forester·Robert Tang·Jing Tao

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Abstract

We study the SL(2,R)-infimal lengths of simple closed curves on half-translation surfaces. Our main result is a characterization of Veech surfaces in terms of these lengths. We also revisit the "no small virtual triangles" theorem of Smillie and Weiss and establish the following dichotomy: the virtual triangle area spectrum of a half-translation surface either has a gap above zero or is dense in a neighborhood of zero. These results make use of the auxiliary polygon associated to a curve on a half-translation surface, as introduced by Tang and Webb.

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Max Forester, Robert Tang, Jing Tao. 2016-05-05. Veech surfaces and simple closed curves. https://arxiv.org/abs/1605.01772

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