Ōshima, Hideaki A homotopy group of the symmetric space SO(2n)/U(n). (English) Zbl 0549.57022 Osaka J. Math. 21, 473-475 (1984). The purpose of this paper is to prove \(\pi_{2n+1}(SO(2n)/U(n))={\mathbb{Z}}_ 2 \oplus {\mathbb{Z}}_{n!/2}\) for \(n\equiv 2 (mod 4)\). It solves an ambiguity in the paper of B. Harris [Trans. Am. Math. Soc. 106, 174-184 (1963; Zbl 0117.165)]. Cited in 4 Documents MSC: 57T20 Homotopy groups of topological groups and homogeneous spaces 55Q52 Homotopy groups of special spaces Keywords:(2n\(+1)st\) homotopy group of SO(2n)/U(n) Citations:Zbl 0117.165 PDFBibTeX XMLCite \textit{H. Ōshima}, Osaka J. Math. 21, 473--475 (1984; Zbl 0549.57022)