Brayton Gray

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1. The purpose of this paper is to examine the smash powers of a two-cell complex P = S2m−1 ∪θ e when localized at primes grater than 3. We have two applications in mind. We intend to introduce Samelson and Whitehead products into the homotopy groups with coefficient in P given by πk(X;P ) = [Σ k−2nP,X] for k ≥ 2n: Neisendorfer did this in the case that n =(More)
We first describe Krull-Schmidt theorems decomposing H spaces and simply-connected co-H spaces into atomic factors in the category of pointed nilpotent p-complete spaces of finite type. We use this to construct a 1-1 correspondence between homotopy types of atomic H spaces and homotopy types of atomic co-H spaces, and construct a split fibration which(More)
Cohen, Moore, and Neisendorfer’s work on the odd primary homotopy theory of spheres and Moore spaces, as well as the first author’s work on the secondary suspension, predicted the existence of a p-local fibration S2n−1 −→ T −→ ΩS2n+1 whose connecting map is degree pr . In a long and complex monograph, Anick constructed such a fibration for p ≥ 5 and r ≥ 1.(More)
It is easy to see that the map just described is a phantom map. Indeed, restrict it to the first n stages of the telescope, and then deform that portion to the right into X, x {n}. This is a deformation retraction. Since X, x {n) is sent to the base point in VEX,, the assertion follows. Thus 0 is one phantom map which is easy to describe. We will show that(More)