Khovanov homology and its Torsion

Abstract

The Khovanov homology is a powerful link invariant which is a bigraded homology invariant and a categorization of the Jones polynomial. Many links including alternating links are known to be homologically slim or simply H-slim. Shumakovitch studied torsion of Khovanov homology, especially proving every H-slim link is weakly torsion thin. In this thesis, we show that every quasi-alternating link $\It{L}$ is torsion thin in Shumakovitch`s sense. We prove this by showing there is no $It{Z_{4}}$-torsion in $\It{H(L)}$, which can be achieved from a modified version of Lee`s differential on the Khovanov homology and Shumakovitch`s tool used to eliminate torsions.