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A homotopy group of the symmetric space SO(2n)/U(n). (English) Zbl 0549.57022

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)].

MSC:

57T20 Homotopy groups of topological groups and homogeneous spaces
55Q52 Homotopy groups of special spaces

Citations:

Zbl 0117.165
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