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On Hilali’s conjecture related to Halperin’s. (English) Zbl 1353.55007

The Hilali conjecture states that if \(X\) is a simply connected elliptic CW complex, then the sum of the rational Betti numbers is at least as large as the sum of the ranks of the homotopy groups. Here elliptic means that both sums are finite. The conjecture has been proved to be correct for some interesting spaces: pure spaces (Hilali), hyper elliptic spaces (de Bobadilla, Fresán, Muñoz and Murillo) and two-stages spaces (Amann), but is unsolved for general elliptic spaces. Here the authors investigate the conjecture for coformal spaces and some manifolds of low dimension.

MSC:

55P62 Rational homotopy theory
55T05 General theory of spectral sequences in algebraic topology
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