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} }
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.
19 Citations
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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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