Virtual 1-domination of 3-manifolds

TL;DR

This paper proves that every closed oriented 3-manifold can be mapped onto by a finite cover of any given hyperbolic 3-manifold with degree 1, improving previous results on virtual domination.

Contribution

It introduces an enhanced connection principle in good pants constructions to establish virtual 1-domination, advancing the understanding of 3-manifold mappings.

Findings

Every closed oriented 3-manifold is virtually 1-dominated by any hyperbolic 3-manifold.

Improves previous results from virtual 2-domination to virtual 1-domination.

Utilizes a new enhanced connection principle in good pants constructions.

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.