Geometry and Topology of Surfaces by Sébastian Baader2021 | ISBN: 3985470006 | English | 88 pages | PDF | 3 MB
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 groupsand Travaux de Thurston sur les surfaces, we tried to include 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
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