MSc Thesis Talk 3:30 pm, Seminar Hall Teichmuller Theory and the Nielson Thurston Classification Theorem Neetal Neel Chennai Mathematical Institute. 190418 Abstract The main aim of this talk is to give an idea of the NielsonThurston Classification Theorem and its proof. In the first half of my talk, I will start with the definition of the mapping class group and the well known classification of the isometry group of the upper half plane, PSL(2,R). I will define the Teichmuller space of a closed,orientable surface S_g. I will introduce measured foliations and quadratic differentials and state the existence and uniqueness of Teichmuller mappings. Next, I will discuss the Teichmuller metric and the action of the mapping class group on the Teichmuller space. In the second half, I will state the strategy of Lipman Bers' proof of the NielsonThurston Classification Theorem and describe the importance of this theorem in 3manifold theory. Time permitting, I will give a sketch of the proof of the theorem.
