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On conjectures of Moore and Serre in the case of torsion-free suspensions

Published online by Cambridge University Press:  24 October 2008

Paul Selick
Paul Selick
Affiliation:
The University of Western Ontario, London, Ontario, Canada
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Extract

Let p be a prime. A space X is said to have a homotopy exponent at p if multiplication by pr annihilates the p-torsion of πn(X) for some non-negative integer r independent of n. X is said to have totally finite rational homotopy if ⊕n πn (X) ⊗ ℚ is a finite vector space. Moore has conjectured that these properties are related for finite simply connected CW complexes.

Moore's Conjecture. A space having the homotopy type of a finite simply connected CW complex has a homotopy exponent at p if and only if it has totally finite rational homotopy.

For convenience I will divide the conjecture into its two implications so that I can refer to each separately.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 94 , Issue 1 , July 1983 , pp. 53 - 60
Copyright
Copyright © Cambridge Philosophical Society 1983

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