Ebook: Geometry and Topology of Surfaces

These lecture notes cover the classification of hyperbolic structures and measured foliations on surfaces in a minimalist way. While the inspiration is obviously taken from the excellent books Primer on mapping class groups and Travaux de Thurston sur les surfaces, the author aimed at including a little bit more of hyperbolic trigonometry, including a proof of Basmajian's identity on the orthogeodesic spectrum, while keeping the rest short.

Keywords: mapping class group, Dehn twist, pseudo-Anosov diffeomorphism, hyperbolic surface, Basmajian identity, measured foliation, Teichmüller theory, Thurston classification