Investigation of properties of the limit sets of fuchsiangroups

In this thesis, the limit sets of Fuchs groups which are discrete subsets of the group of Möbius transformations, are investigated. In the first section, basic topological definitions are given. In the second section, the group of Möbius transformations is defined and classified by their geometrical action on extended complex plane. In the third section, it is studied hyperbolic plane models such as upper half plane model and Poincaré disk model, which will be frequently used in this thesis. In the fourth section, it is given the definition of a Fuchsian group and is investigated its basic properties. In the last section, the concept of the limit set of a Fuchsian group is defined and its properties are examined. At the end of this section, it is given an example of a Fuchsian group whose limit set is a Cantor set.