Hyperbolic links are not generic

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.