Does Khovanov homology detect the unknot?
Matthew Hedden, Liam Watson
TL;DR
This paper proves that Khovanov homology can identify the unknot within a broad class of knots, including many satellite knots like the Whitehead double, enhancing its utility in knot detection.
Contribution
It establishes that Khovanov homology detects the unknot for a large class of knots, extending previous results to include satellite knots such as the Whitehead double.
Findings
Khovanov homology detects the unknot in a wide class of knots.
Includes unknotting number one knots and satellite knots.
Applies to knots like the Whitehead double.
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.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Connective tissue disorders research