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

Hanspeter Fischer¹, David G. Wright²
Fund. Math. 179 (2003), 267-282
doi:10.4064/fm179-3-5

Abstract: 
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.

MSC (2000): 57N99, 57S30, 20F99.
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Department of Mathematical Sciences
Ball State University
Muncie, IN 47306, U.S.A.
Department of Mathematics
Brigham Young University
Provo, UT 84602, U.S.A.