International Mathematics Research Notices

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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This Article Abstract Full Text (PDF) Alert me when this article is cited Alert me if a correction is posted Services Email this article to a friend Similar articles in this journal Alert me to new issues of the journal Add to My Personal Archive Download to citation manager Request Permissions How to cite this article Google Scholar Articles by Fisher, D. Articles by Silberman, L. Social Bookmarking          What's this?