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3-primary exponents

Published online by Cambridge University Press:  24 October 2008

Joseph A. Neisendorfer
Joseph A. Neisendorfer
Affiliation:
Institute for Advanced Study, Princeton
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Extract

The purpose of this paper is to show that 3n annihilates the 3-primary component of the homotopy groups of the 2n + 1-dimensional sphere. In the terminology of (2) and (3), S2n+1 has exponent 3n at 3.

In fact, a stronger result is proved. Localize at 3 and let Ω2nS2n + 1〈2n + 1〉 denote the 2n-fold loop space of the 2n + 1-connected cover of S2n+1. Then Ω2nS2n + 1〈2n + 1〉 has a null homotopic 3n-th power map.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 90 , Issue 1 , July 1981 , pp. 63 - 83
Copyright
Copyright © Cambridge Philosophical Society 1981

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References

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