A note on the localization of $J$-groups

Abstract

Let JO(X) = KO(X)/T O(X) be the J-group of a connected finite CW complex X. Using Atiyah-Tall [5], we obtain two computable formulae of T O(X) (p) , the localization of T O(X) at a prime p. Then we show how to use those two formulae of T O(X) (p) to find the J-orders of elements of KO(X), at least the 2 and 3 primary factors of the canonical generators of JO(CP m ). Here CP m is the complex projective space. 1991 Mathematics Subject Classification: Primary 55Q50, 55R50.