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Proceedings of the American Mathematical Society

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

 

 

A note on infinite loop space multiplications


Author: Rainer M. Vogt
Journal: Proc. Amer. Math. Soc. 85 (1982), 297-298
MSC: Primary 55P47
MathSciNet review: 652462
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Abstract: A monoid $ M$ is known to be abelian iff its multiplication $ M \times M \to M$ is a homomorphism. We prove the corresponding result for homotopy-everything $ H$-spaces, e.g. infinite loop spaces: For a homotopy-everything $ H$space $ X$ each $ n$-ary operation $ {X^n} \to X$ is a homotopy homomorphism, i.e. a homomorphism up to homotopy and all higher coherence conditions.


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DOI: https://doi.org/10.1090/S0002-9939-1982-0652462-1
Keywords: Homotopy-everything $ H$-spaces, infinite loop space, homotopy homomorphism
Article copyright: © Copyright 1982 American Mathematical Society