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Exponents and suspension

Published online by Cambridge University Press:  26 July 2002

DON STANLEY
DON STANLEY
Affiliation:
UMR 0751 ‘AGAT’ du CNRS à l'Université de Lille 1, France. Department of Mathematical Sciences, University of Alberta, Canada. e-mail: stanley@math.ualberta.ca
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Abstract

Let X be a finite CW-complex. We show that the image of the homotopy groups of X under suspension have an exponent at every prime. As a corollary we recover Long's result that finite H-spaces have exponents at all primes. We show that the stable homotopy groups of X have an exponent at p if and only if X is rationally equivalent to a point. This allows us to construct many examples of spaces with infinite dimensional rational homotopy groups and without an exponent at any prime. These examples further support Moore's conjecture.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 133 , Issue 1 , July 2002 , pp. 109 - 116
Copyright
2002 Cambridge Philosophical Society

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