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arXiv:1908.06187 [math.GT]AbstractReferencesReviewsResources

Hyperbolic knots are not generic

Yury Belousov, Andrei Malyutin

Published 2019-08-16Version 1

We show that the proportion of hyperbolic knots among all of the prime knots of $n$ or fewer crossings does not converge to $1$ as $n$ approaches infinity. Moreover, we show that if $K$ is a nontrivial knot then the proportion of satellites of $K$ among all of the prime knots of $n$ or fewer crossings does not converge to $0$ as $n$ approaches infinity.

Comments: Preliminary version, 4 pages
Categories: math.GT
Subjects: 57M25
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