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Proceedings of the American Mathematical Society

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

 

 

A theorem on injectivity of the cup product


Author: John C. Wood
Journal: Proc. Amer. Math. Soc. 37 (1973), 301-304
MSC: Primary 55G05
MathSciNet review: 0307239
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Abstract: We prove that if a space X has abelian or sufficiently abelian fundamental group, then the cup product $ {H^1}(X) \wedge {H^1}(X) \to {H^2}(X)$ is injective, giving an inequality between the associated Betti numbers. This generalises to a theorem of injectivity of the k-fold cup product on $ {H^n}(X)$, given that the kth order Whitehead product on $ {\pi _n}(X)$ is trivial or torsion.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0307239-8
Keywords: Fundamental group, Whitehead products, cup products, Betti numbers
Article copyright: © Copyright 1973 American Mathematical Society