Homology, Homotopy and Applications

Volume 16 (2014)

Number 1

A purely homotopy-theoretic proof of the Blakers-Massey Theorem for $n$-cubes

Pages: 333 – 339

DOI: https://dx.doi.org/10.4310/HHA.2014.v16.n1.a18


Brian A. Munson (Department of Mathematics, U.S. Naval Academy, Annapolis, Maryland, U.S.A.)


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


Published 2 June 2014