Abstract
We prove that a translation surface that has two transverse parabolic elements has a totally real trace field. As a corollary, nontrivial Veech groups that have no parabolic elements do exist.
The proof follows Veech's viewpoint on Thurston's construction of pseudo-Anosov diffeomorphisms
Citation
Pascal Hubert. Erwan Lanneau. "Veech groups without parabolic elements." Duke Math. J. 133 (2) 335 - 346, 1 June 2006. https://doi.org/10.1215/S0012-7094-06-13326-4
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