Domination by geometric 4-manifolds

TL;DR

This paper investigates conditions under which one closed orientable 4-manifold can be mapped onto another, especially focusing on cases where the manifolds are geometric or fiber over surfaces, to understand domination relations.

Contribution

It provides new insights into domination relations among 4-manifolds, particularly in the context of geometric structures and fibered manifolds.

Findings

Characterization of domination by geometric 4-manifolds

Criteria for domination when manifolds fiber over surfaces

Results on domination relations in specific geometric contexts

Abstract

We consider aspects of the question "when is an orientable closed 4-manifold $Y$ dominated by another such manifold $X$", focusing on the cases when $X$ is geometric or fibres non-trivially over an orientable surface.