English

Low height geodesics and the Markoff spectrum

Geometric Topology 2010-05-14 v2 Number Theory

Abstract

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.

Keywords

Cite

@article{arxiv.math/0410197,
  title  = {Low height geodesics and the Markoff spectrum},
  author = {Thomas A. Schmidt and Mark Sheingorn},
  journal= {arXiv preprint arXiv:math/0410197},
  year   = {2010}
}

Comments

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 This paper has been withdrawn by the authors.