On the Spaces $O(4n)/\textit{Sp}$ and $\textit{Sp}(n)/O$, and the Bott Maps

Bott maps and the complex projective plane: a construction of R. Wood’s equivalences

“…Thus we shall give another proof of (0.1) which does not use vector bundle theory. This work may be regarded as a continuation of [10] and [11], and indeed our proof of (0.1) is accomplished by the techniques used there. A by-product of our work is the result that, even for n < oo, the maps χ° and χ^p induce isomorphisms of homotopy groups in sufficiently low dimensions.…”

“…Throughout this paper we shall keep the notation of [10] and [11]. In particular, we denote by comm{A, B) the commutator ABA~λB~ι.…”