English

Khovanov homology: torsion and thickness

Geometric Topology 2007-05-23 v2 Algebraic Topology

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.

Keywords

Cite

@article{arxiv.math/0402402,
  title  = {Khovanov homology: torsion and thickness},
  author = {Marta M. Asaeda and Jozef H. Przytycki},
  journal= {arXiv preprint arXiv:math/0402402},
  year   = {2007}
}

Comments

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)