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Publications mathématiques de l'IHÉS

, Volume 113, Issue 1, pp 97–208 | Cite as

Khovanov homology is an unknot-detector

  • P. B. Kronheimer
  • T. S. Mrowka
Article

Abstract

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.

Keywords

Modulus Space Spectral Sequence Floer Homology KHOVANOV Homology Hopf Link 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© IHES and Springer-Verlag 2011

Authors and Affiliations

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

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