Hyperbolic structures on surfaces and geodesic currents

Javier Aramayona, Christopher J. Leininger

Research output: Chapter in Book/Report/Conference proceedingChapter

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 languageEnglish (US)
Title of host publicationAlgorithmic and geometric topics around free groups and automorphisms
PublisherBirkhäuser/Springer, Cham
Pages111-149
Number of pages39
StatePublished - 2017

Publication series

NameAdv. Courses Math. CRM Barcelona
PublisherBirkhäuser/Springer, Cham

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    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.