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Actions of arithmetic groups on homology spheres and acyclic homology manifolds
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Bridson, Martin R., Grunewald, Fritz and Vogtmann, Karen (2014) Actions of arithmetic groups on homology spheres and acyclic homology manifolds. Mathematische Zeitschrift, 276 (1-2). pp. 387-395. doi:10.1007/s00209-013-1205-2
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WRAP-actions-arithmetic-homology-spheres-acyclic-manifolds-Vogtmann-2014.pdf - Accepted Version - Requires a PDF viewer. Download (704Kb) | Preview |
Official URL: http://doi.org/10.1007/s00209-013-1205-2
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 .
| Item Type: | Journal Article | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||||||
| Divisions: | Faculty of Science > Mathematics | ||||||||
| Journal or Publication Title: | Mathematische Zeitschrift | ||||||||
| Publisher: | Springer | ||||||||
| ISSN: | 0025-5874 | ||||||||
| Official Date: | February 2014 | ||||||||
| Dates: |
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| Date of first compliant deposit: | 30 October 2019 | ||||||||
| Volume: | 276 | ||||||||
| Number: | 1-2 | ||||||||
| Page Range: | pp. 387-395 | ||||||||
| DOI: | 10.1007/s00209-013-1205-2 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Access rights to Published version: | Restricted or Subscription Access |
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