Hyperbolic covering knots

Abstract

Given any knot $k$, there exists a hyperbolic knot $\tilde{k}$ with arbitrarily large volume such that the knot group $\pi k$ is a quotient of $\pi \tilde{k}$ by a map that sends meridian to meridian and longitude to longitude. The knot $\tilde{k}$ can be chosen to be ribbon concordant to $k$ and also to have the same Alexander invariant as $k$.