Extended Adams-Hilton’s construction

Yves Félix and Jean-Claude Thomas

Vol. 128 (1987), No. 2, 251–263

DOI: 10.2140/pjm.1987.128.251

Abstract

Let FEB be a Hurewicz fibration. The homotopy lifting property defines (up to homotopy) an action of the H-space ΩB on the fibre F which makes H_∗(F) into a H_∗(ΩB)-module. Suppose B is connected. We prove that if EB is the cofibre of a map g : W → E where W is a wedge of spheres, then the reduced homology of F, H_∗(F) is a free H_∗(ΩB)-module generated by H_∗(W). This result implies in particular a characterization of aspherical groups.

Mathematical Subject Classification 2000

Primary: 55R20

Milestones

Received: 6 December 1985

Revised: 11 June 1986

Published: 1 June 1987