Minimal models of loop spaces and suspensions
type: Item
instance of: scholarly article
title: Minimal models of loop spaces and suspensions
zbMATH Open document ID: 0808.55009
DOI: 10.1007/BF02568356
author: Martin Arkowitz
author: Gregory Lupton
published in: Manuscripta Mathematica
publication date: 1994-01-31T00:00:00Z
full work available at URL: https://eudml.org/doc/155852
review text: This paper gives the solution to the 2 following problems: (1) Let \(X\) be a space. Determine the Sullivan minimal model for the loop multiplication \(\mu_ x : \Omega X \times \Omega X \to \Omega X\) and the Quillen model for the suspension comultiplication \(\nabla X : \Sigma X \to \Sigma X \vee \Sigma X\). (2) Let \(\psi : A \to A \otimes A\) be an associative comultiplication of a graded commutative algebra and let \(\varphi : L \to L \sqcup L\) be an associative comultiplication of a 1-connected graded Lie algebra \(L\); describe spaces \(X\) and \(Y\) such that \(\psi\) is \((\mu_ x)_ *\) and \(\varphi\) is \((\nabla Y)_ *\).
Mathematics Subject Classification ID: 55P62
Mathematics Subject Classification ID: 55P45
Mathematics Subject Classification ID: 55P40
Mathematics Subject Classification ID: 55P35
zbMATH DE Number: 492758
zbMATH Keywords: Sullivan minimal model for the loop multiplication
zbMATH Keywords: Quillen model for the suspension comultiplication
zbMATH Keywords: comultiplication
zbMATH Keywords: graded Lie algebra
reviewed by: Yves Félix
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 492758