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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 | ||||||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||||||
| Library of Congress Subject Headings (LCSH): | Arithmetic groups , Homology theory, Acyclic models | ||||||||||||
| Journal or Publication Title: | Mathematische Zeitschrift | ||||||||||||
| Publisher: | Springer | ||||||||||||
| ISSN: | 0025-5874 | ||||||||||||
| Official Date: | February 2014 | ||||||||||||
| Dates: |
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| 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 | ||||||||||||
| RIOXX Funder/Project Grant: |
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