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)
type: Item
instance of: scholarly article
title: 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)
zbMATH Open document ID: 0681.55012
DOI: 10.1007/BF02765897
author: Jean Lannes
author: Lionel Schwartz
published in: Israel Journal of Mathematics
publication date: 1989-01-01T00:00:00Z
review text: 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 \(H^*(p;{\mathbb{Z}}_ 2)\).
Mathematics Subject Classification ID: 55Q05
Mathematics Subject Classification ID: 55S10
Mathematics Subject Classification ID: 55T20
Mathematics Subject Classification ID: 55R05
zbMATH DE Number: 4115533
zbMATH Keywords: Steenrod algebra
zbMATH Keywords: abelian 2-groups
zbMATH Keywords: instable algebra
zbMATH Keywords: classifying
zbMATH Keywords: space
zbMATH Keywords: nilpotent mod 2 cohomology
zbMATH Keywords: 1-connected space of finite type
zbMATH Keywords: homotopy groups
zbMATH Keywords: nilpotent fibration
reviewed by: Yves Félix
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4115533