Maps between Seifert fibered spaces of infinite \(\pi_ 1\)
type: Item
instance of: scholarly article
title: Maps between Seifert fibered spaces of infinite \(\pi_ 1\)
zbMATH Open document ID: 0815.57002
published in: Pacific Journal of Mathematics
publication date: 1994-05-24T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 57M12
Mathematics Subject Classification ID: 57N10
zbMATH DE Number: 572470
zbMATH Keywords: maps between closed aspherical Seifert fibered spaces
zbMATH Keywords: vertical pinches
zbMATH Keywords: map of nonzero degree
zbMATH Keywords: branched covering
author: Yongwu Rong
reviewed by: Bruno Zimmermann
MaRDI profile type: Publication
full work available at URL: pjm.1993.160.143
OpenAlex ID: W2070289729
DOI: 10.2140/PJM.1993.160.143
description: scientific article; zbMATH DE number 572470