“…Th results of the paper show the importance of the homotopy type of Ω(n, p). In [1], [2], [4] and [5] we have described the homotopy type of Ω i,0 (n, p) for i = max{n − p + 1, 1} in terms of orthogonal groups and Stiefel manifolds. Although available only in the case of fold-maps, we will construct a simpler spectrum in Section 10 whose stable homotopy group is a direct summand of O(n, P ; Ω i,0 , Ω i,0 ) (respectively N(n, P ; Ω i,0 , Ω i,0 )) and also construct the corresponding classifying space.…”