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Jørgensen Lemma

In this thesis we will first do some classification of the elements in \(PSL(2,\mathbb{R})\). After that we will introduce the notion of Fuchsian groups, i. e. a discrete subgroup of \( PSL( 2, \mathbb{R})\), and prove two criteria for discreteness in \(PSL(2,\mathbb{R})\). One of them is the Jørgensen Inequality, which is the main theorem in this thesis. Finally we look at the special case of equality in the Jørgensen inequality.

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Year: 2016

Author : Fabian Cejka

Prof. Dr. Anna Wienhard
Gye-Seon Lee