KO-theory of certain real Grassmannians (Q2762834)

A complete description of the structure of the ring \(KO^0(G_2(\mathbb{R}^n))\) for \(n=4\) and \(5\), is given. The proof is more involved than that given by \textit{C. F. M.~Ribeiro} [Proc. Lond. Math. Soc., III. Ser. 59, No. 1, 182-208 (1989; Zbl 0677.55004)].NEWLINENEWLINENEWLINEFirst some elementary properties of topological K-theory of finite CW-complexes are considered, then the \(\tilde K O^{-i}\)-groups of the Grassmannians \(G(4,2)\) and \(G(5,2)\) are calculated using the associated spectral sequences of Atiyah-Hirzebruch (for \(i=2,3,4\)) and the KU-theory of \(G_2(\mathbb{R}^4)\) for \(i=5,6,7\).