Heegaard Floer Homology is a useful invariant for three manifolds, and it has many variants that can be used to study four dimensional cobordism and knots in three spheres. In this talk I will first introduce Heegaard decomposition and Heegaard diagram and state some basic properties of them. Then, I will make an analogy to the Lagrangian Floer Homology to define the ingredients of the Heegaard Floer Homology. Finally, I will define the hat version of Heegaard Floer chain complex and homology.
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