The structure of the Hurewicz homomorphism (Q2734867)

The authors study the Hurewicz homomorphism from the viewpoint of the spectral sequence of a Postnikov tower and work in the category of pointed spaces which have the homotopy type of a simple connected (or simple) based CW-complex with locally-finite homology. In order to illustrate results obtained in the paper let us ask ourselves when the Hurewicz homomorphism \(h_n: \pi_n(X) \to H_n(X)\) is an isomorphism in all dimensions? Then the answer is the following statement: The only simple, noncontractible space, for which \(h_n\) is an isomorphism in all dimensions is the circle \(S^1\). Analogous questions are studied when the Hurewicz homomorphism is monomorphism, split monomorphism, epimorphism, and split epimorphism.NEWLINENEWLINEFor the entire collection see [Zbl 0960.00050].