On stable cohomotopy groups of compact spaces II

In the present paper we study properties of compact Hausdorff spaces preserved by maps f:X→Y inducing isomorphisms of stable cohomotopy groups for almost all m>0. The homomorphism depends only on the stable shape morphism f∈ShStab(X,Y) generated by f. Consequently, we try to distinguish and characterize invariants of morphisms in ShStab with the mentioned attribute.