A Study of Heegaard Floer Homologies

Abstract

This thesis is entirely a literature review and aims to be a gateway into the theory of Heegaard Floer homology. These homology groups are powerful invariants for closed oriented 3-manifolds. The thesis initially deals with some of the theoretical background necessary to understand the definitions of Floer Homology. An outline of Morse theory and Morse homology is given at the very beginning of the thesis. Basics of symplectic topology are discussed in an attempt to gain an understanding of the significant tools being applied. Subsequently, different kinds of Floer homology theories are reviewed. The remainder of this thesis outlines a combinatorial algorithm due to Sarkar and Wang for calculating Heegaard Floer homology, coupled with an example to understand the concept better.