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 π s m ( f ) : π s m ( Y ) → π s m ( X ) for almost all m > 0 . The homomorphism π s m ( f ) : π s m ( Y ) → π s m ( X ) 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.