Virtual domination of $3$–manifolds

Abstract

For any closed oriented hyperbolic $\mathfrak{3}$–manifold $M$ and any closed oriented $\mathfrak{3}$–manifold $N$, we show that $M$ admits a finite cover $M^{\prime }$ such that there exists a degree-$\mathfrak{2}$ map $f:M^{\prime }\to N$, ie $M$ virtually $\mathfrak{2}$–dominates $N$.