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. © 2011 IHES and Springer-Verlag.
CITATION STYLE
Kronheimer, P. B., & Mrowka, T. S. (2011). Khovanov homology is an unknot-detector. Publications Mathematiques de l’Institut Des Hautes Etudes Scientifiques, 113(1), 97–208. https://doi.org/10.1007/s10240-010-0030-y
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