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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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Official URL: http://doi.org/10.1007/s00209-013-1205-2

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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, 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:
DateEvent
February 2014Published
7 August 2013Available
7 February 2013Accepted
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:
Project/Grant IDRIOXX Funder NameFunder ID
UNSPECIFIED[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266
UNSPECIFIEDRoyal Societyhttp://dx.doi.org/10.13039/501100000288
DMS-0204185National Science Foundationhttp://dx.doi.org/10.13039/501100008982

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