A purely homotopy-theoretci proof of the Blakers-Massey theorem for $n$-cubes

Abstract

Goodwillie’s proof of the Blakers-Massey Theorem for n- cubes relies on a lemma whose proof invokes transversality. The rest of his proof follows from general facts about cubes of spaces and connectivities of maps. We present a purely homotopytheoretic proof of this lemma. The methods are elementary, using a generalization and modification of an argument originally due to Puppe used to prove the Blakers-Massey Theorem for squares.