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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Higher homotopy commutativity and extension of maps

Author: F. D. Williams
Journal: Proc. Amer. Math. Soc. 26 (1970), 664-670
MSC: Primary 55.40
MathSciNet review: 0273613
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Abstract: Let $ X$ denote the cartesian product of based spaces, $ X = {X_1} \times \cdots \times {X_n}$, and $ A = {X_1} \vee \cdots \vee {X_n}$, the subspace consisting of their one-point union. Further, let $ g:A \to Y$ be a map, for $ Y$ any based space. This article develops a criterion for the extendibility of $ g$ to a map $ G:X \to Y$. The criterion is in terms of higher products which live in the Pontryagin ring of $ \Omega Y$, the loop space of $ Y$.

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Keywords: Homotopy commutativity, loop space, suspension, $ H$-space, homology ring, higher products, Grassmann manifold
Article copyright: © Copyright 1970 American Mathematical Society