On the classification of rational homotopy types of elliptic spaces with homotopy Euler characteristic zero for dim \(< 8\)
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\( \,X \leq 7\).
scientific article; zbMATH DE number 5996091