Maps between Seifert fibered spaces of infinite<i>π</i>₁

Abstract

A theorem of A. Edmonds says that any nonzero degree map between closed surfaces is homotopic to a composition of a pinch map and a branched covering. Here we consider the analogous problem in dimension three. We prove that any nonzero degree map between P 2 -irreducible Seifert fibered spaces of infinite x is homotopic to a composition of "vertical pinches" and a fiber preserving branched covering, except for a few cases which we describe completely. In particular, any such degree one map is homotopic to a composition of vertical pinches.