An elementary construction of Anick’s fibration

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 suspen-sion, predicted the existence of a p–local fibration S2n1 ! T2n1 !S2nC1 whose connecting map is degree pr. In a long and complex monograph, Anick constructed such a fibration for p 5 and r 1. Using new methods we give a much more conceptual construction which is also valid for p D 3 and r 1. We go on to establish an H space structure on T2n1 and use this to construct a secondary EHP sequence for the Moore space spectrum. 55P45, 55P40, 55P3