Khovanov homology is an unknot-detector
Publications Mathématiques de l'IHÉS, Tome 113 (2011), pp. 97-208.

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.

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     author = {Kronheimer, P. B. and Mrowka, T. S.},
     title = {Khovanov homology is an unknot-detector},
     journal = {Publications Math\'ematiques de l'IH\'ES},
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     publisher = {Springer-Verlag},
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     year = {2011},
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Kronheimer, P. B.; Mrowka, T. S. Khovanov homology is an unknot-detector. Publications Mathématiques de l'IHÉS, Tome 113 (2011), pp. 97-208. doi : 10.1007/s10240-010-0030-y. http://archive.numdam.org/articles/10.1007/s10240-010-0030-y/

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