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James-Hopf Invariants, Anick's Spaces, and the Double Loops on Odd Primary Moore Spaces

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Published:2000-06-01
Printed: Jun 2000
• Joseph Neisendorfer
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Abstract

Using spaces introduced by Anick, we construct a decomposition into indecomposable factors of the double loop spaces of odd primary Moore spaces when the powers of the primes are greater than the first power. If $n$ is greater than $1$, this implies that the odd primary part of all the homotopy groups of the $2n+1$ dimensional sphere lifts to a $\mod p^r$ Moore space.
 MSC Classifications: 55Q52 - Homotopy groups of special spaces 55P35 - Loop spaces

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