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)|
|Title of host publication||Algorithmic and geometric topics around free groups and automorphisms|
|Number of pages||39|
|State||Published - 2017|
|Name||Adv. Courses Math. CRM Barcelona|
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.