## Groups generated by reflections and aspherical manifolds not covered by Euclidean space.(English)Zbl 0531.57041

The paper presents a very interesting new construction of proper actions of Coxeter groups on contractible manifolds. This construction is applied to give classes of counterexamples in every dimension $$\geq 4$$ to the following conjecture. The universal cover of any closed aspherical manifold is homeomorphic to Euclidean space [F. E. A. Johnson, Proc. Camb. Philos. Soc. 75, 165-173 (1974; Zbl 0278.57006)]. So there are in every dimension $$\geq 4$$ contractible manifolds not homeomorphic to Euclidean space admitting a proper free action of some discrete group with compact orbit space.
Reviewer: H.Abels

### MSC:

 57S30 Discontinuous groups of transformations 57N15 Topology of the Euclidean $$n$$-space, $$n$$-manifolds ($$4 \leq n \leq \infty$$) (MSC2010) 54H15 Transformation groups and semigroups (topological aspects)

Zbl 0278.57006
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