Maps between Seifert fibered spaces of infinite π₁

Yongwu Rong

Vol. 160 (1993), No. 1, 143–154

DOI: 10.2140/pjm.1993.160.143

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 P²-irreducible Seifert fibered spaces of infinite π₁ 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.

Mathematical Subject Classification 2000

Primary: 55R55

Secondary: 55M25, 57M12, 57N10

Milestones

Received: 10 June 1991

Revised: 14 July 1992

Published: 1 September 1993