Homotopy associativity of sphere extensions

Abstract

Throughout this paper, we work in the category of (p-localized) spaces having the homotopy type of connected CW-complexes of finite type with base point. We consider a principal bundlewhere G n = SU(n), U(n) or Sp(ri) and d=l,l or 2 respectively. In this case, the bundle is obtained as an induced bundle by a mapping / of base space S 2dll~l from the classical group extension as follows: To avoid a confusion with an integer modp, we adopt the notation "a property P at 459