Commutative rings, algebraic topology, graded Lie algebras and the work of Jan-Erik Roos
type: Item
instance of: scholarly article
title: Commutative rings, algebraic topology, graded Lie algebras and the work of Jan-Erik Roos
zbMATH Open document ID: 0574.18008
DOI: 10.1016/0022-4049(85)90001-5
author: David J. Anick
author: Stephen Halperin
published in: Journal of Pure and Applied Algebra
publication date: 1985-01-01T00:00:00Z
review text: For a 1-connected CW complex of finite type X topologists have been interested in the graded algebra \(H_*(\Omega X;{\mathbb{Q}})\), \(\Omega\) X being the loop space of X. Algebraists have studied the graded algebra \(Ext^*_ R(k,k)\), (R,m,k) being a local ring. It has been realized that the two fields - rational homotopy theory and local rings - share a common body of techniques but also of theorems. This article is written in honour to Jan-Erik Roos who was the first to realize the strong connection between the two fields. The article overviews results achieved in this area (on both sides) for the last decades.
Mathematics Subject Classification ID: 18G15
Mathematics Subject Classification ID: 13D03
Mathematics Subject Classification ID: 55P35
Mathematics Subject Classification ID: 13-02
Mathematics Subject Classification ID: 18-02
Mathematics Subject Classification ID: 55-02
Mathematics Subject Classification ID: 17B70
zbMATH DE Number: 3916532
zbMATH Keywords: Poincaré series
zbMATH Keywords: survey. Roos, J.-E
zbMATH Keywords: graded algebra
zbMATH Keywords: loop space
zbMATH Keywords: rational homotopy
zbMATH Keywords: local rings
Wikidata QID: Q115364461
MaRDI profile type: Publication
full work available at URL: 0022-4049(85)90001-5
OpenAlex ID: W2080686774
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description: scientific article; zbMATH DE number 3916532