Subject: A question to the forum Date: Mon, 31 May 2004 19:47:12 +0400 (MSD) From: Podkorytov Semen To: dmd1@lehigh.edu Yesterday evening, I have discovered the following. Let Z be a loop space. Suppose pi_1 (Z) is finitely generated and has no 2-torsion. Then Z admits a map to a simply connected space Y such that the induced map pi_i (Z) to pi_i (Y) is a split monomorphism for every i > 1. Is this fact known to anybody?