Heegaard floer homolojisine giriş

Heegaard Floer homology for a closed, oriented three-manifold $Y$ is defined using Heegaard diagrams and a certain holomorphic curve count in the spirit of Lagrangian Floer homology. For each $s\in Spin^c(Y)$, similar constructions give different versions of homology groups $\widehat{HF}(Y,s)$, $HF^{\infty}(Y,s)$, $HF^-(Y,s)$, and $HF^+(Y,s)$, each of which is an invariant of the underlying three-manifold $Y$. The theory also contains a knot invariant, a smooth four-manifold invariant, and a contact three-manifold invariant besides other things.In this thesis, we focus on the definition of Heegaard Floer homology for a closed, oriented three-manifold $Y$ and the necessary topological tools to define it. The basics of knot Floer homology, an invariant of oriented, nullhomologous knots and links in closed, oriented three-manifolds are also discussed. In addition, we briefly mention another invariant called Khovanov homology for oriented links $L$ which seems to be related to knot Floer homology.