Abstract
The projectivity of the Whitehead square wn = [in, in] in π2n-1(SN) has been studied by Randall [6] who proved that if wn is projective then n must be a power of 2 or one less than a power of 2. Here we solve the question in the even case, proving by means of bo homology:Theorem. if and only if n = 1, 2, 4.
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