Virtual Domination of 3-manifolds III

TL;DR

This paper proves that any cusped hyperbolic 3-manifold can be virtually 8-dominated by a finite cover, meaning there exists a finite cover that admits a degree-8 map onto any compact 3-manifold with torus boundary.

Contribution

It establishes the existence of finite covers of hyperbolic 3-manifolds that admit degree-8 maps onto arbitrary 3-manifolds with torus boundary, advancing understanding of virtual domination.

Findings

Existence of finite covers with degree-8 maps

Virtual domination of 3-manifolds

Extension to manifolds with torus boundary

Abstract

We prove that for any oriented cusped hyperbolic 3-manifold $M$ and any compact oriented 3-manifold $N$ with tori boundary, there exists a finite cover $M'$ of $M$ that admits a degree-8 map $f:M'\to N$, i.e. $M$ virtually 8-dominates $N$.