Khovanov homology is an unknot-detector

Author(s)
Kronheimer, P. B.; Mrowka, Tomasz S.
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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.
Date issued
2011-11
URI
http://hdl.handle.net/1721.1/70474
Department
Massachusetts Institute of Technology. Department of Mathematics
Journal
Publications Mathématiques de L'IHÉS
Publisher
Springer-Verlag
Citation
Kronheimer, P. B., and T. S. Mrowka. “Khovanov Homology Is an Unknot-detector.” Publications mathématiques de l’IHÉS 113.1 (2011): 97–208. Web. 27 Apr. 2012. © 2011 IHES and Springer-Verlag
Version: Author's final manuscript
ISSN
0073-8301
1618-1913
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