On three-manifolds dominated by circle bundles

TL;DR

This paper characterizes three-manifolds dominated by circle bundles or products, providing a classification based on coverings, Thurston geometries, and algebraic properties of their fundamental groups.

Contribution

It offers a complete classification of three-manifolds dominated by products or circle bundles, linking geometric, topological, and algebraic criteria.

Findings

A three-manifold is dominated by a product iff it is finitely covered by a product or a connected sum of S^2×S^1.

Characterization in terms of Thurston geometries and algebraic properties of fundamental groups.

Identification of three-manifolds dominated by non-trivial circle bundles and those with presentable-by-products groups.

Abstract

We determine which three-manifolds are dominated by products. The result is that a closed, oriented, connected three-manifold is dominated by a product if and only if it is finitely covered either by a product or by a connected sum of copies of the product of the two-sphere and the circle. This characterization can also be formulated in terms of Thurston geometries, or in terms of purely algebraic properties of the fundamental group. We also determine which three-manifolds are dominated by non-trivial circle bundles, and which three-manifold groups are presentable by products.