×

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)

Citations:

Zbl 0278.57006
PDF BibTeX XML Cite
Full Text: DOI Link