Topological realizations of chain complexes. II: The rational case
type: Item
instance of: scholarly article
title: Topological realizations of chain complexes. II: The rational case
zbMATH Open document ID: 0692.55014
author: Justin R. Smith
published in: Pacific Journal of Mathematics
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.pjm/1102650287
review text: This paper addresses the following question: Given a group G and a QG- projective chain complex T, does there exist a topological space X with fundamental group isomorphic to G whose equivariant chain complex is T? The paper develops an algebraic obstruction theory for answering this question. In an important special case, the answer is affirmative: namely, when the canonical map \(X\to K(G,1)\) admits a left-inverse up to homotopy. This paper is a continuation of earlier work of the author in Part I [Topology Appl. 22, 301-313 (1986; Zbl 0589.55009)].
Mathematics Subject Classification ID: 55U15
Mathematics Subject Classification ID: 55P91
Mathematics Subject Classification ID: 55U99
Mathematics Subject Classification ID: 18G35
zbMATH DE Number: 4133120
zbMATH Keywords: DGA-coalgebra
zbMATH Keywords: realizations of equivariant chain complexes
zbMATH Keywords: fundamental group
reviewed by: Peter J. Kahn
MaRDI profile type: Publication
OpenAlex ID: W1989655873
DOI: 10.2140/PJM.1989.138.169
description: scientific article; zbMATH DE number 4133120