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On the question of genericity of hyperbolic knots and links
by
Andrei Malyutin
Steklov Inst. St.Petersburg
A well-known conjecture in knot theory says that the proportion of hyperbolic knots among all of the prime knots of n or fewer crossings approaches 1 as n approaches infinity. We show that this conjecture contradicts several other plausible conjectures, including the 120-year-old conjecture on additivity of the crossing number of knots under connected sum and the conjecture that the crossing number of a satellite knot is not less than that of its companion. Also, we show that the proportion of hyperbolic links among all of the prime links of n or fewer crossings does not tend to 1 as n approaches infinity.
Date received: January 2, 2019
Copyright © 2019 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cbpq-38.