Generalized orbifold Euler characteristics of symmetric orbifolds and covering spaces.
Generalized universal covering spaces and the shape group
If a paracompact Hausdorff space X admits a (classical) universal covering space, then the natural homomorphism φ: π₁(X) → π̌₁(X) from the fundamental group to its first shape homotopy group is an isomorphism. We present a partial converse to this result: a path-connected topological space X admits a generalized universal covering space if φ: π₁(X) → π̌₁(X) is injective. This generalized notion of universal covering p: X̃ → X enjoys most of the usual properties, with the possible exception of evenly...
Gradients de Heegaard sous-logarithmiques d’une variété hyperbolique de dimension trois et fibres virtuelles
J. Maher a montré qu’une variété hyperbolique de dimension compacte sans bord, connexe et orientable fibre virtuellement sur le cercle si et seulement si elle admet une famille infinie de revêtements finis de genre de Heegaard borné. En s’appuyant sur la démonstration de Maher, cet article présente un théorème donnant une condition suffisante pour qu’un revêtement fini d’une variété hyperbolique compacte de dimension contienne une fibre virtuelle, qui s’exprime en fonction du degré du revêtement...
Group structure in finite coverings of compact solenoidal groups.
Groups acting on covering spaces
Group-theoretic conditions under which closed aspherical manifolds are covered by Euclidean space
Hass, Rubinstein, and Scott showed that every closed aspherical (irreducible) 3-manifold whose fundamental group contains the fundamental group of a closed aspherical surface, is covered by Euclidean space. This theorem does not generalize to higher dimensions. However, we provide geometric tools with which variations of this theorem can be proved in all dimensions.