Geodesic
An Operad Action on Infinite Loop Space Multiplication
Canadian journal of mathematics, Tome 29 (1977) no. 6, pp. 1208-1216

Voir la notice de l'article provenant de la source Cambridge University Press

It is well-known that an infinite loop space is an H-space whose multiplication enjoys nice properties concerning associativity and commutativity. A practical way of identifying infinite loop spaces is the utilization of May's recognition principle [3; 4]. To apply this principle, one requires an E∞-operad action on a space X; this action gives rise to various multiplications on X. In this note, it is shown that such multiplications enjoy an operad action up to homotopy that encodes the associativity and commutativity information, and that May's delooping theorem may be applied to them. We refer to [3] for the terminology of operads and monads. 
Lada, Thomas. An Operad Action on Infinite Loop Space Multiplication. Canadian journal of mathematics, Tome 29 (1977) no. 6, pp. 1208-1216. doi: 10.4153/CJM-1977-120-9
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[1] 1. Boardman, J. M. and Vogt, R. M., Homotopy-everything H-spaces, Bull. Amer. Math. Soc. 74 (1968), 1117–1122. Google Scholar

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[3] 3. May, J. P., The geometry of iterated loop spaces, Lecture Notes in Mathematics 271 (Springer- Verlag, 1972). Google Scholar

[3] 3. May, J. P. Ex spaces, group completions, and permutative categories, London Mathematical Society Lecture Note Series II, p. 61–94 (Cambridge University Press, 1974). Google Scholar

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