The genericity conjecture for hyperbolic knots
The genericity conjecture for hyperbolic knots
Let be a positive integer, and consider all prime knots with or fewer crossings. The genericity conjecture for hyperbolic knots. The percentage of these knots that are hyperbolic approaches as 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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