Rationally elliptic spaces with isomorphic cohomology algebras. (Q1420638)

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 \(m(A^*)\).