On J-orders of elements of KO(CPm)

Abstract

Let $KO\left(C{P}^m\right)$ be the $KO$-ring of the complex projective space $C{P}^m$. By means of methods of rational $D$-series [4], a formula for the $J$-orders of elements of $KO\left(C{P}^m\right)$ is given. Explicit formulas are given for computing the $J$-orders of the canonical generators of $KO\left(C{P}^m\right)$ and the $J$-order of any complex line bundle over $C{P}^m$.