Khovanov homology is conjectured to distinguish torus knots, twist knots, and Legendrian simple knots, with supporting evidence from exhaustive checks showing no counterexamples among 2.2 billion knots up to 20 crossings.
Stabilization in the braid groups ii transversal simplicity of knots
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Conjectures on the Khovanov Homology of Torus Knots, Twist Knots, and Legendrian Simple Knots
Khovanov homology is conjectured to distinguish torus knots, twist knots, and Legendrian simple knots, with supporting evidence from exhaustive checks showing no counterexamples among 2.2 billion knots up to 20 crossings.