Subject: response to B. Gray's question Date: Thu, 01 May 2003 13:09:11 -0400 (EDT) From: Jean-Pierre Meyer To: dmd1@lehigh.edu Dear Brayton, In an old paper (Barcus, W. D. & Meyer, J.-P., The suspension of a loop space, Am. J. Math.,80, 1958, 895-920), we prove a theorem related to your question: we show there is a fibration SLX--> X with fiber LX*LX Since then, I have seen a couple of simpler proofs of this fact, but I do not have the references. Jean-Pierre PS. I should have added that the projection is the canonical "evaluation" map and X is any based space.