Topology and geometry of 2 and 3-manifolds

Abstract

In this project we study two approaches to the structure theorem of automorphisms of surfaces, one is a geometric method given by Thurston and second is a topological approach developed by Allen Hatcher. The structure theorem classi es automorphism into one of the following types, those that are either periodic, reducible or pseudo-Anosov. This is a generalization of the classi fication of automorphisms of a torus to higher genus surfaces. This theorem is also used to study 3-manifolds.