Mathematical Research Letters

Volume 16 (2009)

Number 6

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

Pages: 991 – 994

DOI: http://dx.doi.org/10.4310/MRL.2009.v16.n6.a6

Author

Matthew Hedden (Michigan State University)

Abstract

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.

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