Publications mathématiques de l'IHÉS

, Volume 113, Issue 1, pp 97–208

Khovanov homology is an unknot-detector



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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© IHES and Springer-Verlag 2011

Authors and Affiliations

  1. 1.Harvard UniversityCambridgeUSA
  2. 2.Massachusetts Institute of TechnologyCambridgeUSA

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