Introduction to gromov hyperbolic spaces

Abstract

In this thesis, we provide an introduction to Gromov Hyperbolic spaces. We will look at some properties of these spaces and some examples. Then we look at the properties of geodesic triangles in hyperbolic spaces. We will also look into the boundary of hyperbolic spaces. Towards the end, we will prove an important theorem on the variance of hyperbolicity under qusai -isometries. Using this we will prove two theorems on hyperbolic groups.