Khovanov homology is an unknot-detector
Kronheimer, P. B.1 ; Mrowka, T. S.2
1 Harvard University Cambridge, MA, 02138 USA
2 Massachusetts Institute of Technology Cambridge, MA, 02139 USA
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.

DOI : 10.1007/s10240-010-0030-y
Kronheimer, P. B. 1 ; Mrowka, T. S. 2

1 Harvard University Cambridge, MA, 02138 USA
2 Massachusetts Institute of Technology Cambridge, MA, 02139 USA 
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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://www.numdam.org/articles/10.1007/s10240-010-0030-y/

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