%0 Journal Article
%T Khovanov homology is an unknot-detector
%A P. B. Kronheimer
%A T. S. Mrowka
%J Mathematics
%D 2010
%I arXiv
%X We prove that a knot is the unknot if and only if its reduced Khovanov cohomology has rank 1. The proof has two steps. We show first that there is a spectral sequence beginning with the reduced Khovanov cohomology and abutting to a knot homology defined using singular instantons. We then show that the latter homology is isomorphic to the instanton Floer homology of the sutured knot complement: an invariant that is already known to detect the unknot.
%U http://arxiv.org/abs/1005.4346v1