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On The Geometry Of Fuchsian Groups, Hala Alaqad

Theses

In this Master thesis we consider the discrete groups with emphasis on the geometry of discrete groups, which lie at the intersection between Hyperbolic Geometry, Topology, Abstract Algebra, and Complex Analysis. Fuchsian groups are discrete subgroups of the group PSL(2,ℝ) of linear fractional transformations of one complex variable, which is isomorphic to a quotient topological group: PSL(2,ℝ)≅SL(2,ℝ)/{±I}. Here SL (2,ℝ) is special linear group and I is the identity. We study discrete groups, in particular, Fuchsian groups. We present the geometric properties of Fuchsian groups such as fundamental domains, compactness, and Dilichlet tessellations. In addition, we also present some algebraic …