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The 3-primary classifying space of the fiber of the double suspension

By Stephen D. Theriault and Communicated Paul Goerss

Abstract

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

Year: 2013
OAI identifier: oai:CiteSeerX.psu:10.1.1.352.6072
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