Negatively curved groups and their applications : an honors thesis (HONRS 499)
William W. Malone · Cardinal Scholar (Ball State University) · 2005
The goal of this thesis is to explore geometric group theory which is a fairly recent area of mathematics in which geometric techniques (specifically the theory of geodesic metric spaces) are applied to algebraic objects (specifically infinite finitely presented groups).In the early 1980's Mikhail Gromov, James Cannon, and others developed methods analogous to the curvature methods in differential geometry, but applicable to a broader category of metric spaces. These techniques have subsequently proven valuable in understanding certain previously difficult groups by studying their Cayley Graphs (a geometric object derived from the group). We will define and describe these techniques and give some examples of their use.