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Cocompact spherical-Euclidean spaceform groups of infinite VCD. (English) Zbl 0794.57016

This paper exhibits closed manifolds \(M\) covered by \(S^{2n-1}\times \mathbb{R}^ k\) for all \(n\geq 2\) and for sufficiently large \(k\), with fundamental groups of infinite virtual cohomological dimension. These examples are based on results of M. S. Raghunathan [Math. Ann. 266, 403-419 (1984; Zbl 0513.22008)] on lattices in covers of spin and symplectic groups and address a problem first raised by Wall.

MSC:

57S30 Discontinuous groups of transformations
18G20 Homological dimension (category-theoretic aspects)
20J05 Homological methods in group theory
22E40 Discrete subgroups of Lie groups
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