A note on the localization of \(J\)-groups (Q1306514)

This paper gives information about \(\widetilde{JO}(X)\), the reduced \(J\)-group of a compact CW-space \(X\). To this end the author localizes the quotient map \(\widetilde{KO}(X)\to \widetilde{JO}(X)\) at a prime \(p\) and offers two formulae to compute the resulting kernel. He then demonstrates how this approach can be applied effectively to obtain information about \(\widetilde{JO}({\mathbb C}P^m)\), using as input the known group \(\widetilde{KO}({\mathbb C}P^m)\).