Rationally elliptic spaces with isomorphic cohomology algebras.
type: Item
instance of: scholarly article
title: Rationally elliptic spaces with isomorphic cohomology algebras.
zbMATH Open document ID: 1043.55005
author: Tetsu Nishimoto
author: H. Shiga
author: Toshihiro Yamaguchi
published in: Journal of Pure and Applied Algebra
publication date: 2004-02-02T00:00:00Z
review text: A simply connected space is called rationally elliptic if the dimensions of the cohomology algebra, \(H^*(X;\mathbb{Q})\), and of the homotopy Lie algebra, \(\pi_*(X)\otimes \mathbb{Q}\), are finite. In [Trans. Am. Math. Soc. 230, 173--199 (1977; Zbl 0364.55014)], \textit{S. Halperin} proved that rationally elliptic spaces satisfy Poincaré duality. In the paper under review, the authors consider the set \(M(A^*)\) of rationally elliptic homotopy types \(X\) whose cohomology algebra is isomorphic to a fixed Poincaré duality algebra \(A^*\) over \(\mathbb{Q}\). Motivated by a question asked by Y. Félix, they construct an example of such an algebra \(A^*\) with an infinite set \(m(A^*)\).
Mathematics Subject Classification ID: 55P62
zbMATH DE Number: 2035902
zbMATH Keywords: rational homotopy
zbMATH Keywords: elliptic space
reviewed by: Daniel Tanré
MaRDI profile type: Publication
full work available at URL: j.jpaa.2003.07.010
OpenAlex ID: W2137709999
cites work: Problems and conjectures in rational homotopy theory: A survey
cites work: Q4505020
cites work: An arithmetic characterization of the rational homotopy groups of certain spaces
cites work: Finiteness in the Minimal Models of Sullivan
cites work: Elliptic rational spaces whose cohomologies and homotopies are isomorphic
cites work: Infinitesimal computations in topology
DOI: 10.1016/J.JPAA.2003.07.010
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description: scientific article; zbMATH DE number 2035902