### Abstract

This paper contains lecture notes from a course given by the authors at CRM (Barcelona) in 2012 at the workshop "Automorphisms of Free Groups: Geometry, Topology, and Dynamics''. The notes mainly cover the compactification of Teichmüller space via geodesic currents on a surface, due originally to Bonahon. The first section covers hyperbolic structures and Fuchsian groups. The second section describes Teichmüller space, measured geodesic laminations, and the `classical' construction of Thurston's compactification of Teichmüller space. The third section covers geodesic currents and Bonahon's description of Thurston's compactification. The final section covers a number of generalizations of these ideas to other related settings, particularly negatively curved and flat metrics on surfaces, along with free groups.

Original language | English (US) |
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Title of host publication | Algorithmic and geometric topics around free groups and automorphisms |

Publisher | Birkhäuser/Springer, Cham |

Pages | 111-149 |

Number of pages | 39 |

State | Published - 2017 |

### Publication series

Name | Adv. Courses Math. CRM Barcelona |
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Publisher | Birkhäuser/Springer, Cham |

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## Cite this

Aramayona, J., & Leininger, C. J. (2017). Hyperbolic structures on surfaces and geodesic currents. In

*Algorithmic and geometric topics around free groups and automorphisms*(pp. 111-149). (Adv. Courses Math. CRM Barcelona). Birkhäuser/Springer, Cham.