The Milgram non-operad

Michael Brinkmeier

Annales de l'institut Fourier (1999)

  • Volume: 49, Issue: 5, page 1427-1438
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Brinkmeier, Michael. "The Milgram non-operad." Annales de l'institut Fourier 49.5 (1999): 1427-1438. <http://eudml.org/doc/75388>.

@article{Brinkmeier1999,
abstract = {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.},
author = {Brinkmeier, Michael},
journal = {Annales de l'institut Fourier},
keywords = {-operad; permutohedron; free -fold loop spaces},
language = {eng},
number = {5},
pages = {1427-1438},
publisher = {Association des Annales de l'Institut Fourier},
title = {The Milgram non-operad},
url = {http://eudml.org/doc/75388},
volume = {49},
year = {1999},
}

TY - JOUR
AU - Brinkmeier, Michael
TI - The Milgram non-operad
JO - Annales de l'institut Fourier
PY - 1999
PB - Association des Annales de l'Institut Fourier
VL - 49
IS - 5
SP - 1427
EP - 1438
AB - 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.
LA - eng
KW - -operad; permutohedron; free -fold loop spaces
UR - http://eudml.org/doc/75388
ER -

References

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  1. [1] C. BALTEANU, Z. FIEDOROWICZ, R. SCHWÄNZL, R. VOGT, Iterated monoidal categories, preprint 98-035, Universität Bielefeld, 1998. 
  2. [2] H.-J. BAUES, Geometry of loop spaces and the cobar-construction, Mem. Amer. Math. Soc., 230 (1980). Zbl0473.55009MR81m:55010
  3. [3] C. BERGER, Opérades cellulaires et espaces de lacets itérés, Ann. Inst. Fourier, 46 (1996), 1125-1157. Zbl0853.55007MR98c:55011
  4. [4] C. BERGER, Combinatorial models for real configuration spaces and en-operads, Cont. Math., 202 (1997), 37-52. Zbl0860.18001MR98j:18014
  5. [5] J.M. BOARDMAN, R.M. VOGT, Homotopy-everything h-spaces, Bull. Amer. Math. Soc., 74 (1968), 1117-1122. Zbl0165.26204MR38 #5215
  6. [6] J.M. BOARDMAN, R.M. VOGT, Homotopy invariant algebraic structures on topological spaces, Lecture Notes in Math. 347 (Springer, Berlin), 1973. Zbl0285.55012MR54 #8623a
  7. [7] Y. HEMMI, Higher homotopy commutativity of H-spaces and the mod p torus theorem, Pac. J. Math., 149 (1991), 95-111. Zbl0691.55007MR92a:55010
  8. [8] J.P. MAY, The geometry of iterated loop spaces, Lecture Notes in Math. 271 (Springer, Berlin), 1972. Zbl0244.55009MR54 #8623b
  9. [9] C.A. MCGIBBON, Higher forms of homotopy commutativity and finite loop spaces, Math. Zeitschrift, 201 (1989), 363-374. Zbl0682.55006MR90f:55019
  10. [10] R.J. MILGRAM, Iterated loop spaces, Ann. of Math., 84 (1966), 386-403. Zbl0145.19901MR34 #6767
  11. [11] J.D. STASHEFF, Homotopy associativity of h-spaces, I, Trans. Amer. Math. Soc., 108 (1963), 275-292. Zbl0114.39402MR28 #1623
  12. [12] F.D. WILLIAMS, Higher homotopy-commutativity, Trans. Amer. Math. Soc., 139 (1969), 191-206. Zbl0185.27103MR39 #2163

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