Maps between Seifert fibered spaces of infinite \(\pi_ 1\) (Q1325287)

By a theorem of Edmonds, any nonzero degree map between closed surfaces is homotopic to a composition of a pinch map and a branched covering. In the present paper, an analogous result is proved in dimension 3 for maps \(f : M \to N\) between closed aspherical Seifert fibered spaces \((\mathbb{P}^ 2\)-irreducible with infinite fundamental group): any map of nonzero degree between such 3-manifolds is homotopic to a composition of ``vertical pinches'' and a branched covering (which is fiber preserving except maybe in the case where \(N\) is a Euclidean manifold and Seifert fibrations are not unique). In particular, any degree one map is homotopic to a composition of vertical pinches.