Homology, Homotopy and Applications
Volume 16 (2014)
A purely homotopy-theoretic proof of the Blakers-Massey Theorem for $n$-cubes
Pages: 333 – 339
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 homotopy-theoretic 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.
excision, Blakers-Massey theorem, Triad connectivity theorem
2010 Mathematics Subject Classification