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The Quarterly Journal of Mathematics Advance Access originally published online on July 18, 2006
The Quarterly Journal of Mathematics 2007 58(1):31-45; doi:10.1093/qmath/hal013
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© 2006. Published by Oxford University Press. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

ON FREYD'S GENERATING HYPOTHESIS

Mark Hovey{dagger}

Department of Mathematics, Wesleyan University, Middletown, CT 06459, USA

{dagger} E-mail: hovey{at}member.ams.org

Received 7 February 2006; revised 15 May 2006
  Abstract

Freyd's generating hypothesis in stable homotopy theory is revisited and new consequences and equivalent forms of it are derived. A surprising such consequence is that I, the Brown–Comenetz dual of the sphere and the source of many counterexamples in stable homotopy, is the cofibre of a self-map of a wedge of spheres. It is also shown that a consequence of the generating hypothesis, that the homotopy of a finite spectrum that is not a wedge of spheres can never be finitely generated as a module over {pi}*S, is in fact true for many finite torsion spectra.


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