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On equivariant J-groups of complex projective spaces with the conjugate involution. (English) Zbl 0546.55018

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

Citations:

Zbl 0503.55005
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