Cohen, F. R.; Peterson, F. P. Suspensions of Stiefel manifolds. (English) Zbl 0555.55010 Q. J. Math., Oxf. II. Ser. 35, 115-119 (1984). Let \(V_{n,k}\) denote the Stiefel manifold of orthogonal k-frames in n- space and let \(CV_{n,k}\) denote its complex analogue. Let \(P_{n,k}={\mathbb{R}}P^{n-1}/{\mathbb{R}}P^{n-k-1}\) and let \(CP_{n,k}={\mathbb{C}}P^{n-1}/{\mathbb{C}}P^{n-k-1}.\) There are inclusions \(P_{n,k}\to V_{n,k}\) and \(\Sigma CP_{n,k}\to CV_{n,k}\) which are stable retracts. Let r(n,k) denote the least r such that \(\Sigma^ rP_{n,k}\) is a retract of \(\Sigma^ rV_{n,k}\) and similarly r(n,k,\({\mathbb{C}})\) in the complex case. The authors obtain bounds on these numbers, thereby answering some questions posed by I. M. James [The topology of Stiefel manifolds, Lond. Math. Soc. Lect. Note Ser. 24 (1976; Zbl 0337.55017)]. Reviewer: V.Snaith Cited in 1 ReviewCited in 1 Document MSC: 55P40 Suspensions 55P42 Stable homotopy theory, spectra Keywords:suspensions of Stiefel manifolds; stunted projective spaces; James numbers; stable retracts Citations:Zbl 0337.55017 PDFBibTeX XMLCite \textit{F. R. Cohen} and \textit{F. P. Peterson}, Q. J. Math., Oxf. II. Ser. 35, 115--119 (1984; Zbl 0555.55010) Full Text: DOI