Gaps in the Milnor-Moore spectral sequence
type: Item
instance of: scholarly article
title: Gaps in the Milnor-Moore spectral sequence
zbMATH Open document ID: 1035.55007
author: Thomas Kahl
author: Lucile Vandembroucq
published in: Bulletin of the Belgian Mathematical Society - Simon Stevin
publication date: 2004-01-22T00:00:00Z
review text: Ljusternik-Schnirelman category cat has the property \({\text{cat}}(X \cup e^n) \leq {\text{cat}}X+1\) where \(X\cup e^n\) is the space \(X\) with the attached cell \(e^n\). The authors prove that this property fails for certain well-known algebraic invariants that approximate cat (such as Toomer invariant \(e\), weak category, \(\sigma{\text{cat}}\)). For example, they construct a space \(Z\) such that \(e(Z)=2\) and \(e(Z\cup e^n)=4\). From these results, the authors deduce that there can be gaps in the Eilenberg-Moore spectral sequence, i.e. one can have \(E^{\infty}_{p,*}=0\) while \(E^{\infty}_{p+1,*}=0\).
Mathematics Subject Classification ID: 55M30
Mathematics Subject Classification ID: 55T20
Mathematics Subject Classification ID: 55P62
zbMATH DE Number: 2031084
zbMATH Keywords: Ljusternik-Schnirelman theory
zbMATH Keywords: Toomer invariant
zbMATH Keywords: Eilenberg-Moore spectral sequence
reviewed by: Yuli Rudyak
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2031084