A note on the localization of J-groups

Abstract

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 $\widetilde{KO}(C{P}^m)$, at least the 2 and 3 primary factors of the canonical generators of $\widetilde{JO}(C{P}^m).$ Here $C{P}^m$ is the complex projective space.

15 pages, Latex2e, to appear in Hiroshima Math. J., 2 (1999)