Author
Bridson, M
Grunewald, F
Vogtmann, K
Journal title
Mathematische Zeitschrift
DOI
10.1007/s00209-013-1205-2
Issue
1-2
Volume
276
Last updated
2023-07-01T05:00:55.02+01:00
Page
387-395
Abstract
We establish lower bounds on the dimensions in which arithmetic groups with torsion can act on acyclic manifolds and homology spheres. The bounds rely on the existence of elementary p-groups in the groups concerned. In some cases, including Sp(2n, ℤ), the bounds we obtain are sharp: if X is a generalized ℤ/3-homology sphere of dimension less than 2n-1 or a ℤ/3-acyclic ℤ/3-homology manifold of dimension less than 2n, and if n ≥ 3, then any action of Sp(2n, ℤ) by homeomorphisms on X is trivial; if n = 2, then every action of Sp(2n, ℤ) on X factors through the abelianization of Sp(4, ℤ), which is ℤ/2. © 2013 Springer-Verlag Berlin Heidelberg.
Symplectic ID
448417
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Publication type
Journal Article
Publication date
01 Feb 2014
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