2
$\begingroup$

Let $K$ be a finite $CW$-complex. Could you give any references or explanations for the following two items? I do not understand. Thanks!

(1). The Chern character from $\tilde{KO}^0(K)$ to the product of the rational cohomology groups $H^{4j}(K)$ is rationally an isomorphism.

(2). Therefore in order for a vector bundle $\xi$ on $K$ to be such that some multiple of it is trivial it is sufficient if the rational Pontryagin classes vanish.

$\endgroup$
2

0

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.