Kakutani, Shin-ichiro On equivariant J-groups of complex projective spaces with the conjugate involution. (English) Zbl 0546.55018 Mem. Fac. Sci., Kochi Univ., Ser. A 5, 1-5 (1984). From the introduction: ”Let G be the group \({\mathbb{Z}}_ 2\). Let \({\mathbb{C}}P^ n_{\tau}\) denote the n-dimensional complex projective space with the G-action given by the conjugation of homogeneous coordinates. In ibid., 4, 23-42 (1983; Zbl 0503.55005), we have proved that the forgetful homomorphism \(^{\sim}_ G({\mathbb{C}}P^ n_{\tau})\to^{\sim}({\mathbb{C}}P^ n)\) is an isomorphism. Let X be a compact G-space with base point. Let \(J_ G(X)\) denote the equivariant J-group and \(J_ G: KO_ G(X)\to J_ G(X)\) the equivariant J- homomorphism. We set \(\tilde J_ G(X)=J_ G(^{\sim}_ G(X))\subset J_ G(X).\) The purpose of this paper is to show that the forgetful homomorphism \(\tilde J_ G({\mathbb{C}}P^ n_{\tau})\to\tilde J({\mathbb{C}}P^ n)\) is an isomorphism”. Reviewer: T.Kobayashi MSC: 55Q50 \(J\)-morphism 55Q91 Equivariant homotopy groups 57S17 Finite transformation groups 55S25 \(K\)-theory operations and generalized cohomology operations in algebraic topology 55R50 Stable classes of vector space bundles in algebraic topology and relations to \(K\)-theory Keywords:n-dimensional complex projective space; conjugation of homogeneous coordinates; equivariant J-group; equivariant J-homomorphism; forgetful homomorphism; isomorphism Citations:Zbl 0503.55005 PDFBibTeX XMLCite \textit{S.-i. Kakutani}, Mem. Fac. Sci., Kochi Univ., Ser. A 5, 1--5 (1984; Zbl 0546.55018)