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

Volume 179 / 2003

Hanspeter Fischer, David G. Wright Fundamenta Mathematicae 179 (2003), 267-282 MSC: 57N99, 57S30, 20F99. DOI: 10.4064/fm179-3-5


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.


  • Hanspeter FischerDepartment of Mathematical Sciences
    Ball State University
    Muncie, IN 47306, U.S.A.
  • David G. WrightDepartment of Mathematics
    Brigham Young University
    Provo, UT 84602, U.S.A.

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