Khovanov homology: torsion and thickness
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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.
33 pages, 26 figures, to appear in Proceedings of the Workshop, ``New Techniques in Topological Quantum Field Theory" Calgary/Kananaskis, Canada, August 2001; Ed. J.Bryden. (Property 1.5 rewritten in e-print)
33 pages, 26 figures, to appear in Proceedings of the Workshop, ``New Techniques in Topological Quantum Field Theory" Calgary/Kananaskis, Canada, August 2001; Ed. J.Bryden. (Property 1.5 rewritten in e-print)