Hyperbolic Geometry: Isometry Groups of Hyperbolic Space
نویسنده
چکیده
The goal of this paper is twofold. First, it consists of an introduction to the basic features of hyperbolic geometry, and the geometry of an important class of functions of the hyperbolic plane, isometries. Second, it identifies a group structure in the set of isometries, specifically those that preserve orientation, and deals with the topological properties of their discrete subgroups. In the final section, we show that if one of these Fuchsian groups satisfies certain conditions, then its quotient space is a 2-manifold for which the hyperbolic plane is a covering space.
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