Vol. 60, No. 1, 1975

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On loop spaces without p torsion

Richard Michael Kane

Vol. 60 (1975), No. 1, 189–201

Let (X,m) be a 1-connected H-space whose loop space ΩX has no p torsion. We study the algebra structure of HX;Zp) and its relation, via the Eilenberg-Moore spectral sequence, to that of H(X;Zp). The module Q(H(X;Zp)) 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;Zp)).

Mathematical Subject Classification
Primary: 55D45
Received: 15 February 1974
Published: 1 September 1975
Richard Michael Kane