Displaying similar documents to “Some remarks concerning the covering numbers of closed manifolds.”

Minimal atlases of manifolds

Alberto Cavicchioli, Luigi Grasselli (1985)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

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Representing open 3-manifolds as 3-fold branched coverings.

José María Montesinos-Amilibia (2002)

Revista Matemática Complutense

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It is proved that the Freudenthal compactification of an open, connected, oriented 3-manifold is a 3-fold branched covering of S, and in some cases, a 2-fold branched covering of S. The branching set is a locally finite disjoint union of strings.

Group-theoretic conditions under which closed aspherical manifolds are covered by Euclidean space

Hanspeter Fischer, David G. Wright (2003)

Fundamenta Mathematicae

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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.