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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm179-3-5,
author = {Hanspeter Fischer and David G. Wright},
title = {Group-theoretic conditions under which closed aspherical manifolds are covered by Euclidean space},
journal = {Fundamenta Mathematicae},
volume = {177},
year = {2003},
pages = {267-282},
zbl = {1055.57032},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm179-3-5}
}
Hanspeter Fischer; David G. Wright. Group-theoretic conditions under which closed aspherical manifolds are covered by Euclidean space. Fundamenta Mathematicae, Tome 177 (2003) pp. 267-282. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm179-3-5/