A purely homotopy-theoretic proof of the Blakers-Massey theorem for \(n\)-cubes

DOI10.4310/HHA.2014.V16.N1.A18zbMATH Open1296.55014arXiv1205.6668MaRDI QIDQ740183

Brian A. Munson

Publication date: 2 September 2014

Published in: Homology, Homotopy and Applications (Search for Journal in Brave)

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.

Full work available at URL: https://arxiv.org/abs/1205.6668

zbMATH Keywords

excisionBlakers-Massey theoremtriad connectivity theorem

Mathematics Subject Classification ID

Homotopy theory (55P99)

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