Hyperbolic links are not generic

Andrei V. Malyutin

Hyperbolic links are not generic

Geometric Topology 2019-07-11 v1

Authors: Andrei V. Malyutin

Abstract

We show that if $K$ is a nontrivial knot then the proportion of satellites of $K$ among all of the prime non-split links of $n$ or fewer crossings does not converge to $0$ as $n$ approaches infinity. This implies in particular that the proportion of hyperbolic links among all of the prime non-split links of $n$ or fewer crossings does not converge to 1 as $n$ approaches infinity. We consider unoriented link types.

Keywords

knot theory

Cite

@article{arxiv.1907.04458,
  title  = {Hyperbolic links are not generic},
  author = {Andrei V. Malyutin},
  journal= {arXiv preprint arXiv:1907.04458},
  year   = {2019}
}

Comments

Preliminary version

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