A note on infinite loop space multiplications
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- by Rainer M. Vogt PDF
- Proc. Amer. Math. Soc. 85 (1982), 297-298 Request permission
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
- J. M. Boardman and R. M. Vogt, Homotopy-everything $H$-spaces, Bull. Amer. Math. Soc. 74 (1968), 1117–1122. MR 236922, DOI 10.1090/S0002-9904-1968-12070-1
- J. M. Boardman and R. M. Vogt, Homotopy invariant algebraic structures on topological spaces, Lecture Notes in Mathematics, Vol. 347, Springer-Verlag, Berlin-New York, 1973. MR 0420609
- Thomas Lada, An operad action on infinite loop space multiplication, Canadian J. Math. 29 (1977), no. 6, 1208–1216. MR 454969, DOI 10.4153/CJM-1977-120-9
- J. M. Boardman and R. M. Vogt, Homotopy invariant algebraic structures on topological spaces, Lecture Notes in Mathematics, Vol. 347, Springer-Verlag, Berlin-New York, 1973. MR 0420609
Additional Information
- © Copyright 1982 American Mathematical Society
- 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