Bott maps and the complex projective plane: A construction of R. Wood's equivalences (Q1070575)

A well-known result of R. Wood in K-theory implies that the unitary group U(\(\infty)\) is homotopy-equivalent to the space of based maps \({\mathbb{P}}_ 2{\mathbb{C}}\to G(\infty)\) where G(\(\infty)\) is either the orthogonal group O(\(\infty)\) or the symplectic group Sp(\(\infty)\). In the present paper an explicit construction of such homotopy equivalences is given, and Wood's theorem is proved by the same method as in the author's previous paper [Publ. Res. Inst. Math. Sci. 19, 317-326 (1983; Zbl 0516.55007)].