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The Quarterly Journal of Mathematics Advance Access originally published online on August 2, 2008
The Quarterly Journal of Mathematics 2009 60(4):461-474; doi:10.1093/qmath/han021
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© 2008. Published by Oxford University Press. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

EXAMPLES OF FREE ACTIONS ON PRODUCTS OF SPHERES

Ian Hambleton{dagger} and Özgün Ünlü {ddagger}

Department of Mathematics and Statistics, McMaster University, Hamilton, ON L8S 4K1, Canada

{dagger} Corresponding author. E-mail: ian{at}math.mcmaster.ca

Received 1 June 2007; revised 21 May 2008
  Abstract

We construct a non-abelian extension {Gamma} of S1 by Z/3 x Z/3, and prove that {Gamma} acts freely and smoothly on S5 x S5. This gives new actions on S5 x S5 for an infinite family P of finite 3-groups. We also show that any finite odd-order subgroup of the exceptional Lie group G2 admits a free smooth action on S11 x S11. This gives new actions on S11 x S11 for an infinite family E of finite groups. We explain the significance of these families P, E for the general existence problem, and correct some mistakes in the literature.

{ddagger} E-mail: unluo{at}math.mcmaster.ca


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