Mathematical Research Letters
Volume 16 (2009)
Khovanov homology of the $2$-cable detects the unknot
Pages: 991 – 994
Inspired by recent work of Grigsby and Werhli, we use the deep geometric content of \ons’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.