Minicurse: Morse Theory

We will introduce the concepts of chain complex and homology and describe them from a Morse theoretical point of view. In particular we will analyze the relation between the homology groups of a manifold and its handle decomposition. A special attention will be paid to the interplay between homology of a three dimensional manifold M and the Heegaard of M. For the sake of completness we will also briefly introduce the concept of cohomology.