SIMPLICIAL RESOLUTIONS AND GANEA FIBRATIONS

In this work, we compare two approximations of a pathconnected space X: the one given by the Ganea spaces G(n)(X) and the one given by the realizations parallel to Lambda X parallel to(n) of the truncated simplicial resolutions induced by the loop-suspension cotriple Sigma Omega. For a simply connected space X, we construct maps parallel to Lambda(center dot)X parallel to(n-1) -> G(n)(X) -> parallel to Lambda(center dot)X parallel to(n) over X, up to homotopy. In the case n = 2, we also prove the existence of a map G(2)(X) -> parallel to Lambda(center dot)X parallel to(1) over X (up to homotopy).