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International Mathematics Research Notices (2008) Vol. 2008 : article ID rnn060, 11 pages, doi:10.1093/imrn/rnn060 published on June 13, 2008
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© The Author 2008. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oxfordjournals.org

Groups Not Acting on Manifolds

David Fisher1 and Lior Silberman2

1 Department of Mathematics, Indiana University, Bloomington, IN 47401, USA
2 School of Mathematics, Institute for Advanced Study, Princeton, NJ 08540, USA

Correspondence: Correspondence to be sent to: fisherdm{at}indiana.edu

In this article, we collect a series of observations that constrain actions of many groups on compact manifolds. In particular, we show that "generic" finitely generated groups have no smooth volume-preserving actions on compact manifolds while also producing many finitely presented, torsion-free groups with the same property.


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