Hyperbolic knots are not generic

Yury Belousov; Andrei Malyutin

Hyperbolic knots are not generic

Geometric Topology 2019-08-20 v1

Authors: Yury Belousov , Andrei Malyutin

Abstract

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.

Keywords

knot theory hyperbolic groups

Cite

@article{arxiv.1908.06187,
  title  = {Hyperbolic knots are not generic},
  author = {Yury Belousov and Andrei Malyutin},
  journal= {arXiv preprint arXiv:1908.06187},
  year   = {2019}
}

Comments

Preliminary version, 4 pages

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