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Khovanov homology: torsion and thickness

Marta M. Asaeda·Jozef H. Przytycki
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Abstract

We partially solve the conjecture by A.Shumakovitch about torsion in the Khovanov homology of prime, non-split links in S^3. 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 and the Hopf link with the Khovanov homology of the diagram via a short exact sequence of homology which splits. Finally we show that our results can be adapted to reduced Khovanov homology and we show that there is a long exact sequence connecting reduced Khovanov homology with unreduced homology.

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Marta M. Asaeda, Jozef H. Przytycki. 2004-07-02. Khovanov homology: torsion and thickness. https://arxiv.org/abs/math/0402402

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