On loop spaces without p torsion

Richard Michael Kane

Vol. 60 (1975), No. 1, 189–201

DOI: 10.2140/pjm.1975.60.189

Abstract

Let (X,m) be a 1-connected H-space whose loop space ΩX has no p torsion. We study the algebra structure of H_∗(ΩX;Z_p) and its relation, via the Eilenberg-Moore spectral sequence, to that of H^∗(X;Z_p). The module Q(H^∗(X;Z_p)) of indecomposables is a module over A^∗(p), the Steenrod algebra. Our main result is to show that, when X is finite, lack of torsion in the loop space is reflected in the A^∗(p) structure of Q(H^∗(X;Z_p)).

Mathematical Subject Classification

Primary: 55D45

Milestones

Received: 15 February 1974

Published: 1 September 1975