Ordering Thurston's geometries by maps of non-zero degree

TL;DR

This paper establishes an ordering of certain 4-manifolds based on maps of non-zero degree and demonstrates that the Kodaira dimension is monotone under these maps, advancing understanding of geometric structures in 4-manifolds.

Contribution

It introduces a new ordering of closed aspherical 4-manifolds with non-hyperbolic Thurston geometries and links this to the monotonicity of Kodaira dimension.

Findings

Ordered 4-manifolds by maps of non-zero degree

Proved Kodaira dimension is monotone under these maps

Applied results to geometric 4-manifolds

Abstract

We obtain an ordering of closed aspherical 4-manifolds that carry a non-hyperbolic Thurston geometry. As application, we derive that the Kodaira dimension of geometric 4-manifolds is monotone with respect to the existence of maps of non-zero degree.