MSc Thesis Talk
3:30 pm, Seminar Hall
Teichmuller Theory and the Nielson Thurston Classification Theorem
Neetal Neel
Chennai Mathematical Institute.
19-04-18

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Abstract

The main aim of this talk is to give an idea of the Nielson-Thurston 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 Nielson-Thurston Classification Theorem and describe the importance of this theorem in 3-manifold theory. Time permitting, I will give a sketch of the proof of the theorem.