Computation of grid homology

Abstract

In this thesis, the main aim is to study a combinatorial approach of knot Floer homology for a given knot K (or a link) in S3, called grid homology. We will define the bigrading structure on the chain complexes, and will show the difference and rela tion between the variants of grid homology. We will show, by a simple example, the invariance of simply blocked grid homologyd GH(G) under stabilization move. We will compute the symmetrized Alexander polynomial of a knot K in S3, a polynomial knot invariant, using grid diagrams. Finally, we will compute grid homology of positive Hopf link.