Veech groups without parabolic elements

Details Veech groups without parabolic elements Veech groups without parabolic elements

2005-03-02

arxiv.org/abs/math/0503047v2

Mathematics

Geometric Topology

7 pages, Corrected typos, to appear in Duke Mathematical Journal

Scientific paper

We prove that a ``bouillabaisse'' surface (translation surface which has two
transverse parabolic elements) has totally real trace field. As a corollary,
non trivial Veech groups which have no parabolic elements do exist. The proof
follows Veech's viewpoint on Thurston's construction of pseudo-Anosov
diffeomorphisms.

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