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# 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

#### Author

#### 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 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.

#### Keywords

excision, Blakers-Massey theorem, Triad connectivity theorem

#### 2010 Mathematics Subject Classification

55P99

Published 2 June 2014