Un 3-polyGEM de cohomologie modulo 2 nilpotente
Jiang, Donghua
Annales de l'Institut Fourier, Tome 54 (2004), p. 1053-1072 / Harvested from Numdam
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On construit un contre-exemple de la conjecture suivante : si la cohomologie modulo 2 réduite d'un polyGEM 1-connexe quelconque est de type fini et si elle n'est pas réduite à (0), alors elle contient au moins un élément non nilpotent.

We give a counter-example of the following conjecture: if the reduced mod 2 cohomology of any 1-connected polyGEM is of finite type and is not trivial, then it contains at least one element of infinite height, i.e., non nilpotent.

Publié le : 2004-01-01
DOI : https://doi.org/10.5802/aif.2043
Classification:  55N99,  55S45,  57T35,  55R20,  55T20
Mots clés: polyGEM, espaces de Milgram, suite spectrale d'Eilenberg-Moore 
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     author = {Jiang, Donghua},
     title = {Un 3-polyGEM de cohomologie modulo 2 nilpotente},
     journal = {Annales de l'Institut Fourier},
     volume = {54},
     year = {2004},
     pages = {1053-1072},
     doi = {10.5802/aif.2043},
     mrnumber = {2111021},
     zbl = {1065.55002},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/AIF_2004__54_4_1053_0}
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Jiang, Donghua. Un 3-polyGEM de cohomologie modulo 2 nilpotente. Annales de l'Institut Fourier, Tome 54 (2004) pp. 1053-1072. doi : 10.5802/aif.2043. http://gdmltest.u-ga.fr/item/AIF_2004__54_4_1053_0/

[1] E.H. Brown; F.P. Peterson Whitehead products and cohomology operations, Quart. J. Math. Oxford Ser. (2), Tome 15 (1964), pp. 116-120 | MR 161341 | Zbl 0124.38401

[2] F. Cohen Communication privée (2003)

[3] E. Dror; Farjoun Cellular spaces, null spaces and homotopy localization, Springer-Verlag, Berlin, Lecture Notes in Mathematics, Tome 1622 (1996) | MR 1392221 | Zbl 0842.55001

[4] Y. Félix; S. Halperin; J.-M. Lemaire; J.-C. Thomas Mod p loop space homology, Invent. Math, Tome 95 (1989) no. 2, pp. 247-262 | MR 974903 | Zbl 0667.55007

[5] J. Grodal The transcendence degree of the mod p cohomology of finite Postnikov systems, Stable and unstable homotopy.Toronto, Fields Inst. (1996), pp. 111-130 | Zbl 0905.55012

[6] L. Kristensen On secondary cohomology operations, Math. Scand, Tome 12 (1963), pp. 57-82 | MR 159333 | Zbl 0118.18303

[7] J. Lannes; Et L. Schwartz À propos de conjectures de Serre et Sullivan, Invent. Math, Tome 83 (1986) no. 3, pp. 593-603 | MR 827370 | Zbl 0563.55011

[8] J. Lannes; Et L. Schwartz Sur les groupes d'homotopie des espaces dont la cohomologie modulo 2 est nilpotente, Israel J. Math, Tome 66 (1989) no. 1-3, pp. 260-273 | MR 1017166 | Zbl 0681.55012

[9] C.A. Mcgibbon; J.A. Neisendorfer On the homotopy groups of a finite-dimensional space, Comment. Math. Helv., Tome 59 (1984) no. 2, pp. 253-257 | MR 749108 | Zbl 0538.55010

[10] J. Milgram The structure over the Steenrod algebra of some 2-stage Postnikov systems, Quart. J. Math. Oxford Ser. (2), Tome 20 (1969), pp. 161-169 | MR 248811 | Zbl 0177.51501

[11] J.W. Milnor; J.C. Moore On the structure of Hopf algebras, Annals of Mathematics (2), Tome 81 (1965), pp. 211-264 | MR 174052 | Zbl 0163.28202

[12] J.-P. Serre Cohomologie modulo 2 des complexes d'Eilenberg-MacLane, Comment. Math. Helv, Tome 27 (1953), pp. 198-232 | MR 60234 | Zbl 0052.19501

[13] L. Smith The cohomology of stable two stage Postnikov systems, Illinois J. Math, Tome 11 (1967), pp. 310-329 | MR 208597 | Zbl 0171.21803

[14] N.E. Steenrod Cohomology operations, Lectures by N.E. Steenrod written and revised by D.B.A. Epstein, Princeton University Press, Princeton (Annals of Mathematics Studies) Tome 50 (1962) | Zbl 0102.38104