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Proceedings of the American Mathematical Society

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A note on infinite loop space multiplications


Author: Rainer M. Vogt
Journal: Proc. Amer. Math. Soc. 85 (1982), 297-298
MSC: Primary 55P47
DOI: https://doi.org/10.1090/S0002-9939-1982-0652462-1
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.


References [Enhancements On Off] (What's this?)

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  • [3] T. Lada, An operad action on infinite loop space multiplication, Canad. J. Math. 29 (1977), 1208-1216. MR 0454969 (56:13211)
  • [4] J. P. May, The geometry of iterated loop spaces, Lecture Notes in Math., vol. 271, Springer-Verlag, Berlin and New York, 1972. MR 0420610 (54:8623b)

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Additional Information

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

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