I'm confused by the following question: f:X\to Y$f:X\to Y$ is a weak homotopy equivalence, that is f_:\pi_(X)\to \pi_(Y) is an isomorphism for any dimensional homotopy groups. However, for the stable homotopy groups, is the homomorphism f_:\pi_^s(X)\to \pi_^s(Y)$f_*:\pi_*(X)\to \pi_*(Y)$ is an isomorphism for any dimensional homotopy groups. However, for the stable homotopy groups, is the homomorphism $f_*:\pi_*^s(X)\to \pi_*^s(Y)$ still an isomorphism?
Any comments are welcome! Many Thanks!