Virtual 1-domination of 3-manifolds

Abstract

It is shown in this paper that given any closed oriented hyperbolic 3-manifold, every closed oriented 3-manifold is mapped onto by a finite cover of that manifold via a map of degree 1, or in other words, virtually 1-dominated by that manifold. This improves a known result of virtual 2-domination. The proof invokes a recently developed enhanced version of the connection principle in good pants constructions.