L-S category and homogeneous spaces
type: Item
instance of: scholarly article
title: L-S category and homogeneous spaces
zbMATH Open document ID: 0701.55012
DOI: 10.1016/0022-4049(90)90099-4
author: Barry Jessup
published in: Journal of Pure and Applied Algebra
publication date: 1990-01-01T00:00:00Z
review text: The author gives some relations between rational Lusternik-Schnirelmann type invariants for homogeneous spaces. For a 1-connected space S, the Milnor-Moore spectral sequence is obtained by filtering the bar construction on the chain differential algebra \(C_*(\Omega S)\) by the bar degree. Toomer and Ginsburg have used this spectral sequence to introduce two numerical invariants: \[ e(S)=\sup \{p| \quad E_{\infty}^{p,*}\neq 0\}\text{ and } \ell (S)=\inf \{p\geq 1| \quad E^{*,*}_{p+1}=E_{\infty}^{*,*}\}. \] With rational coefficients the corresponding invariants are respectively denoted by \(e_ 0| S)\) and \(\ell_ 0| S)\). If G and H are compact, simply connected Lie groups, the author proves that \(cat_ 0(G/H)\leq e_ 0(G_ H)\cdot \ell_{\theta}(G/H)\). He also proves the Halperin's conjecture \((``cat_ 0(G/H)=e_ 0(G/H)'')\) in some particular cases.
Mathematics Subject Classification ID: 55P62
Mathematics Subject Classification ID: 55M30
zbMATH DE Number: 4149150
zbMATH Keywords: Milnor-Moore spectral sequence
zbMATH Keywords: bar construction
zbMATH Keywords: Lie groups
reviewed by: Yves Félix
MaRDI profile type: Publication
full work available at URL: 0022-4049(90)90099-4
OpenAlex ID: W2021312555
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description: scientific article; zbMATH DE number 4149150