Virtual domination of 3-manifolds II

TL;DR

This paper proves that any closed oriented 3-manifold with positive simplicial volume virtually 1-dominates any other closed oriented 3-manifold, extending previous results to more general domains.

Contribution

It establishes a broad virtual domination result for 3-manifolds with positive simplicial volume, generalizing prior work limited to hyperbolic cases.

Findings

Existence of finite covers with degree-1 maps between 3-manifolds.

Extension of virtual domination results beyond hyperbolic manifolds.

Generalization to a wider class of 3-manifolds with positive simplicial volume.

Abstract

For any closed oriented 3-manifold $M$ with positive simplicial volume and any closed oriented 3-manifold $N$, we prove that there exists a finite cover $M'$ of $M$ that admits a degree-1 map $f:M'\to M$, i.e. M virtually 1-dominates N. This result generalizes previous virtual domination results with closed hyperbolic domain to more general domains.