Simple closed geodesics and the study of Teichmüller spaces
Hugo Parlier
Université de Fribourg, Switzerland
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Abstract
The goal of the chapter is to present certain aspects of the relationship between the study of simple closed geodesics and Teichmüller spaces. The set of simple closed geodesics is more than a mere curiosity and has been central in the study of surfaces for quite some time. There are two main themes to the chapter. The first one is the study of the set of simple closed geodesics in contrast with the set of closed geodesics and the second is on systoles, their lengths and related quantities such as the lengths of minimal pants decompositions.