Hyperbolic links are not generic

Andrei V. Malyutin

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arXiv · 1907.04458

Hyperbolic links are not generic

Andrei V. Malyutin

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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.

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Andrei V. Malyutin. 2019-07-09. Hyperbolic links are not generic. https://arxiv.org/abs/1907.04458

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