The Milgram non-operad
Annales de l'Institut Fourier, Tome 49 (1999) no. 5, pp. 1427-1438.

C. Berger affirme avoir construit une structure de E n -opérade sur les permutoèdres de Milgram, dont la monade associée est exactement le modèle de Milgram pour les espaces libres de lacets itérés. Dans ce travail je montre que cet énoncé n’est pas correct.

C. Berger claimed to have constructed an E n -operad-structure on the permutohedras, whose associated monad is exactly the Milgram model for the free loop spaces. In this paper I will show that this statement is not correct.

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Brinkmeier, Michael. The Milgram non-operad. Annales de l'Institut Fourier, Tome 49 (1999) no. 5, pp. 1427-1438. doi : 10.5802/aif.1724. http://www.numdam.org/articles/10.5802/aif.1724/

[1] C. Balteanu, Z. Fiedorowicz, R. Schwänzl, R. Vogt, Iterated monoidal categories, preprint 98-035, Universität Bielefeld, 1998. | MR 1982884 | Zbl 1030.18006

[2] H.-J. Baues, Geometry of loop spaces and the cobar-construction, Mem. Amer. Math. Soc., 230 (1980). | MR 567799 | Zbl 0473.55009

[3] C. Berger, Opérades cellulaires et espaces de lacets itérés, Ann. Inst. Fourier, 46 (1996), 1125-1157. | EuDML 75202 | Numdam | MR 1415960 | Zbl 0853.55007

[4] C. Berger, Combinatorial models for real configuration spaces and en-operads, Cont. Math., 202 (1997), 37-52. | MR 1436916 | Zbl 0860.18001

[5] J.M. Boardman, R.M. Vogt, Homotopy-everything h-spaces, Bull. Amer. Math. Soc., 74 (1968), 1117-1122. | MR 236922 | Zbl 0165.26204

[6] J.M. Boardman, R.M. Vogt, Homotopy invariant algebraic structures on topological spaces, Lecture Notes in Math. 347 (Springer, Berlin), 1973. | MR 420609 | Zbl 0285.55012

[7] Y. Hemmi, Higher homotopy commutativity of H-spaces and the mod p torus theorem, Pac. J. Math., 149 (1991), 95-111. | MR 1099785 | Zbl 0691.55007

[8] J.P. May, The geometry of iterated loop spaces, Lecture Notes in Math. 271 (Springer, Berlin), 1972. | MR 420610 | Zbl 0244.55009

[9] C.A. Mcgibbon, Higher forms of homotopy commutativity and finite loop spaces, Math. Zeitschrift, 201 (1989), 363-374. | EuDML 174058 | MR 999733 | Zbl 0682.55006

[10] R.J. Milgram, Iterated loop spaces, Ann. of Math., 84 (1966), 386-403. | MR 34 #6767 | Zbl 0145.19901

[11] J.D. Stasheff, Homotopy associativity of h-spaces, I, Trans. Amer. Math. Soc., 108 (1963), 275-292. | MR 28 #1623 | Zbl 0114.39402

[12] F.D. Williams, Higher homotopy-commutativity, Trans. Amer. Math. Soc., 139 (1969), 191-206. | MR 39 #2163 | Zbl 0185.27103

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