Simplicial resolutions and Ganea fibrations

Abstract

In this work, we compare two approximations of a path- connected space X: the one given by the Ganea spaces Gn (X) and the one given by the realizations Λ• X n of the trun- cated simplicial resolutions induced by the loop-suspension cotriple ΣΩ. For a simply connected space X, we construct maps Λ• X n−1 → Gn (X) → Λ• X n over X, up to homo- topy. In the case n = 2, we also prove the existence of a map G2 (X) → Λ• X 1 over X (up to homotopy).