Maps which induce the zero map on homotopy

Donald William Kahn

Vol. 15 (1965), No. 2, 537–540

DOI: 10.2140/pjm.1965.15.537

Abstract

The work of Eilenberg and MacLane shows that a map from one space to another may induce the zero map on homotopy groups, yet be essential. The purpose of this paper is to give a characterization of such maps in terms of Postnikov decompositions of the spaces. As applications, we consider what additional information is needed to make such a map null-homotopic, and we prove a proposition concerning Chern classes.

Mathematical Subject Classification

Primary: 55.40

Milestones

Received: 7 April 1964

Published: 1 June 1965