Sur les groupes d'homotopie des espaces dont la cohomologie modulo 2 est nilpotente. (On the homotopy groups of spaces whose cohomology mod 2 is nilpotent)
The main object of this note is to prove a generalization of the theorem of Serre: A 1-connected space of finite type whose mod 2 cohomology is nilpotent (and nontrivial) has infinitely many homotopy groups which are not of odd torsion. The authors show also that for every nilpotent fibration \(F\to^{i}E\to^{p}B\), where B is a connected space and where F, E and B have finite type mod 2 cohomology, the following holds: If a class x belongs to the kernel of \(H^*(i;{\mathbb{Z}}_ 2)\), then some power of x belongs to the ideal generated by Im \(H^*(p;{\mathbb{Z}}_ 2)\).
scientific article; zbMATH DE number 4115533
scientific article