Low height geodesics and the Markoff spectrum

Details Low height geodesics and the Markoff spectrum Low height geodesics and the Markoff spectrum

2004-10-07

arxiv.org/abs/math/0410197v2

Mathematics

Geometric Topology

This has been published. This paper has been withdrawn by the authors.

Scientific paper

We classify, in terms of topology of highest arcs, low height non-simple geodesics on the modular hyperbolic punctured sphere with three elliptic fixed points of order two. Of eight possible types, exactly one consists of geodesics that form a bigon about the cusp; we express all such geodesics in terms of Markoff triples. We also show that any geodesic joining two elliptic fixed points has locally isolated height.

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