A note on the localization of $J$-groups
Copyright policy )A note on the localization of $J$-groups
Let $\widetilde{JO}(X)=\widetilde{KO}(X)/TO(X)$ be the J-group of a connected finite CW complex X. We Obtain two computable formulas of $TO(X)_{(p)}$, the localization of $TO(X)$ at a prime p. Then we show how to use these two formulas of $TO(X)_{(p)}$ to find the J-orders of elements of $\widetilde{KO}(CP^m)$, at least the 2 and 3 primary factors of the canonical generators of $\widetilde{JO}(CP^m).$ Here $CP^m$ is the complex projective space.
15 pages, Latex2e, to appear in Hiroshima Math. J., 2 (1999)
K-Theory and Homology (math.KT), \(J\)-theory, \(J\)-morphism, 55Q50, 55P60, Localization and completion in homotopy theory, 55Q50, 55R50 (primary), 55R50, Mathematics - K-Theory and Homology, FOS: Mathematics, Algebraic Topology (math.AT), Mathematics - Algebraic Topology, Stable classes of vector space bundles in algebraic topology and relations to \(K\)-theory
K-Theory and Homology (math.KT), \(J\)-theory, \(J\)-morphism, 55Q50, 55P60, Localization and completion in homotopy theory, 55Q50, 55R50 (primary), 55R50, Mathematics - K-Theory and Homology, FOS: Mathematics, Algebraic Topology (math.AT), Mathematics - Algebraic Topology, Stable classes of vector space bundles in algebraic topology and relations to \(K\)-theory
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