Khovanov homology of the $2$-cable detects the unknot

@article{Hedden2008KhovanovHO,
  title={Khovanov homology of the \$2\$-cable detects the unknot},
  author={Matthew Hedden},
  journal={Mathematical Research Letters},
  year={2008},
  volume={16},
  pages={991-994}
}
  • M. Hedden
  • Published 28 May 2008
  • Mathematics
  • Mathematical Research Letters
Inspired by recent work of Grigsby and Werhli, we use the deep geometric content of Ozsvath and Szabo's Floer homology theory to provide a short proof that the Khovanov homology of the 2-cable detects the unknot. A corollary is that Khovanov's categorification of the 2-colored Jones polynomial detects the unknot. 
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<abstract abstract-type="TeX"><p> We determine a class of knots, which includes unknotting number one knots, within which Khovanov homology detects the unknot. A corollary is that the Khovanov…
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