Khovanov homology: torsion and thickness

Details Khovanov homology: torsion and thickness Khovanov homology: torsion and thickness

2004-02-25

arxiv.org/abs/math/0402402v2

Mathematics

Geometric Topology

33 pages, 26 figures, to appear in Proceedings of the Workshop, ``New Techniques in Topological Quantum Field Theory" Calgary/

Scientific paper

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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