Abstract. Gray showed that the homotopy fiber Wn of the double suspension S2n−1 E2 − → Ω2S2n+1 has an integral classifying space BWn, which fits in a homotopy fibration S2n−1 E2 − → Ω2S2n+1 ν − → BWn. In addition, after localizing at an odd prime p, BWn is an H-space and if p ≥ 5, then BWn is homotopy associative and homotopy commutative, and ν is an H-map. We positively resolve a conjecture of Gray’s that the same multiplicative properties hold for p = 3 as well. We go on to give some exponent consequences. 1
To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.