Morse Theory and The Morse inequalities

Abstract

This bachelor thesis will give a introduction to Morse theory and the Morse inequalities. Morse theory is a method that can be used to determine the cells in the cell structure of a differentiable manifold. Most of the theory discussed in this thesis will be from Morse theory, written by Milnor. We will be giving a overview of the theory involved and discuss a few examples. In particular will we be looking at the examples of CP^n, RP^n and HP^n. We will also discuss the Morse inequalities. In particular, we will discuss the method of proving these inequalities discovered by Witten.