The virtual Thurston seminorm of 3-manifolds

TL;DR

This paper demonstrates that the Thurston seminorms of all finite covers of an aspherical 3-manifold can classify the manifold as a graph, mixed, or hyperbolic type.

Contribution

It establishes a new method to classify 3-manifolds based on the Thurston seminorms of their finite covers.

Findings

Thurston seminorms determine manifold type.

Finite covers' seminorms classify 3-manifolds.

Provides a classification criterion for aspherical 3-manifolds.

Abstract

We show that the Thurston seminorms of all finite covers of an aspherical 3-manifold determine whether it is a graph manifold, a mixed 3-manifold or hyperbolic.