Does Khovanov homology detect the unknot?

2008/05/28 by Hedden, Matthew, Watson, Liam
#57M25 #57M27 #FOS: Mathematics #Geometric Topology (math.GT) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.0805.4423

Abstract

We determine a wide class of knots, which includes unknotting number one knots, within which Khovanov homology detects the unknot. A corollary is that the Khovanov homology of many satellite knots, including the Whitehead double, detects the unknot.

Related

• Khovanov homology is an unknot-detector
• Khovanov homology of the 2-cable detects the unknot
• Conjectures on the Khovanov Homology of Legendrian and Transversely Simple Knots
• Khovanov homology and rational unknotting
• Two detection results of Khovanov homology on links