Un 3-polyGEM de cohomologie modulo 2 nilpotente
[A 3-polyGEM of nilpotent modulo 2 cohomology]
Annales de l'Institut Fourier, Volume 54 (2004) no. 4, pp. 1053-1072.

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.

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.

DOI: 10.5802/aif.2043
Classification: 55N99, 55S45, 57T35, 55R20, 55T20
Mot clés : polyGEM, espaces de Milgram, suite spectrale d'Eilenberg-Moore
Keywords: polyGEM, Milgram spaces, Eilenberg-Moore spectral sequences
Jiang, Donghua 1

1 LAGA, Institut Galilée, Université Paris Nord, 93430 Villetaneuse (France)
@article{AIF_2004__54_4_1053_0,
     author = {Jiang, Donghua},
     title = {Un {3-polyGEM} de cohomologie modulo 2 nilpotente},
     journal = {Annales de l'Institut Fourier},
     pages = {1053--1072},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {54},
     number = {4},
     year = {2004},
     doi = {10.5802/aif.2043},
     mrnumber = {2111021},
     zbl = {1065.55002},
     language = {fr},
     url = {http://archive.numdam.org/articles/10.5802/aif.2043/}
}
TY  - JOUR
AU  - Jiang, Donghua
TI  - Un 3-polyGEM de cohomologie modulo 2 nilpotente
JO  - Annales de l'Institut Fourier
PY  - 2004
SP  - 1053
EP  - 1072
VL  - 54
IS  - 4
PB  - Association des Annales de l’institut Fourier
UR  - http://archive.numdam.org/articles/10.5802/aif.2043/
DO  - 10.5802/aif.2043
LA  - fr
ID  - AIF_2004__54_4_1053_0
ER  - 
%0 Journal Article
%A Jiang, Donghua
%T Un 3-polyGEM de cohomologie modulo 2 nilpotente
%J Annales de l'Institut Fourier
%D 2004
%P 1053-1072
%V 54
%N 4
%I Association des Annales de l’institut Fourier
%U http://archive.numdam.org/articles/10.5802/aif.2043/
%R 10.5802/aif.2043
%G fr
%F AIF_2004__54_4_1053_0
Jiang, Donghua. Un 3-polyGEM de cohomologie modulo 2 nilpotente. Annales de l'Institut Fourier, Volume 54 (2004) no. 4, pp. 1053-1072. doi : 10.5802/aif.2043. http://archive.numdam.org/articles/10.5802/aif.2043/

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

[2] F. Cohen Communication privée (2003)

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

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

[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

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

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

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

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

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

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

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

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

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

Cited by Sources: