Khovanov Homology: Torsion and Thickness

We partially solve the conjecture by A.Shumakovitch that the Khovanov homology of a nontrivial, prime, non-split link (different from the Hopf link) in S3 has a non-trivial torsion part. We give a size restriction on the Khovanov homology of almost alternating links. We relate the Khovanov homology of the connected sum of a link diagram with the Hopf link to the Khovanov homology of the diagram via a short exact sequence of homology and prove that this sequence splits. Finally, we show that our results can be adapted to reduced Khovanov homology and that there is a long exact sequence connecting reduced Khovanov homology with unreduced homology.