The genericity conjecture for hyperbolic knots

Let nn be a positive integer, and consider all prime knots with nn or fewer crossings. The genericity conjecture for hyperbolic knots. The percentage of these knots that are hyperbolic approaches 100100 as nn approaches infinity. This conjecture is motivated by computational data showing that hyperbolic knots constitute the overwhelming majority of prime knots with small crossing number. The paper states that it contradicts several other plausible conjectures, including additivity of crossing number under connected sum and the assertion that a satellite knot has crossing number at least that of its companion.

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Primary source

Andrei Malyutin, “On the question of genericity of hyperbolic knots”, arXiv:1612.03368 (2016).

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