Christoforos Neofytidis

On three-manifolds dominated by circle bundles

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 S2 × S1. 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.

On stability of non-domination under taking products

We show that non-domination results for targets that are not dominated by products are stable under Cartesian products.

Branched coverings of simply connected manifolds

Abstract We construct branched double coverings by certain direct products of manifolds for connected sums of copies of sphere bundles over the 2-sphere. As an application we answer a question of Kotschick and Loh up to dimension five. More precisely, we show that (1) every simply connected, closed four-manifold admits a branched double covering by a product of the circle with a connected sum of copies of S 2 × S 1 , followed by a collapsing map; (2) every simply connected, closed five-manifold admits a branched double covering by a product of the circle with a connected sum of copies of S 3 × S 1 , followed by a map whose degree is determined by the torsion of the second integral homology group of the target.

Degrees of Self-Maps of Products

Every closed oriented manifold

SETS OF DEGREES OF MAPS BETWEEN SU(2)-BUNDLES OVER THE 5-SPHERE

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Invariant incompressible surfaces in reducible 3-manifolds

is associated with a set of integers

Fundamental groups of aspherical manifolds and maps of non-zero degree

D(M)

On a problem of Hopf for circle bundles over aspherical manifolds with hyperbolic fundamental groups.

, the set of self-mapping degrees of

On a problem of Hopf for circle bundles over negatively curved manifolds

M

Anosov diffeomorphisms of products I. Negative curvature and rational homology spheres

. In this paper we investigate whether a product