On the classification of rational homotopy types of elliptic spaces with homotopy Euler characteristic zero for dim \(< 8\)
type: Item
instance of: scholarly article
title: On the classification of rational homotopy types of elliptic spaces with homotopy Euler characteristic zero for dim \(< 8\)
zbMATH Open document ID: 1234.55010
author: Mamoru Mimura
author: H. Shiga
published in: Bulletin of the Belgian Mathematical Society - Simon Stevin
publication date: 2012-01-10T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.bbms/1323787176
review text: A simply connected space is called elliptic if dim\(\, \pi_*(X)\otimes \mathbb Q<\infty\) and dim\(\, H^*(X;\mathbb Q)<\infty\). Then the homotopy Euler characteristic \(\chi_{\pi} (X) = \sum_p(-1)^p \text{dim}\, \pi_p(X)\otimes \mathbb Q \) is \(\leq 0\). If \(\chi_\pi(X) = 0\) then by a theorem of Halperin the cohomology is the quotient of a graded polynomial algebra divided by a regular sequence. In this paper the authors classify up to rational homotopy equivalences all rational homotopy types of elliptic CW complexes with \(\chi_\pi (X) = 0\) and dim\( \,X \leq 7\).
reviewed by: Yves Félix
Mathematics Subject Classification ID: 55P62
zbMATH DE Number: 5996091
zbMATH Keywords: rational homotopy types
zbMATH Keywords: elliptic space
MaRDI profile type: Publication
Recommended article: Classification of rational homotopy type for 8-cohomological dimension elliptic spaces
Recommended article: The rational homotopy type of elliptic spaces up to cohomological dimension 8
Recommended article: Q3772911
Recommended article: Classification of rational homotopy type for 10-cohomological dimension elliptic spaces
Recommended article: Elliptic spaces with the rational homotopy type of spheres
Recommended article: Q3996239
Recommended article: Elliptic rational spaces whose cohomologies and homotopies are isomorphic
Recommended article: The homotopy type of spaces of rational curves on a toric variety
Recommended article: Q4537948
Recommended article: Q4400720
description: scientific article; zbMATH DE number 5996091