On three-manifolds dominated by circle bundles

Details On three-manifolds dominated by circle bundles On three-manifolds dominated by circle bundles

2012-02-28

arxiv.org/abs/1202.6302v1

Mathematics

Geometric Topology

12 pages

Scientific paper

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.

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