A note on the Hilali conjecture

Abstract

In this short note we observe that the Hilali conjecture holds for two-stage spaces, i.e. we argue that the dimension of the rational cohomology is at least as large as the dimension of the rational homotopy groups for these spaces. We also prove the Hilali conjecture for a class of spaces which puts it into the context of fibrations.

References in corpus (2)

• A conjectured lower bound for the cohomological dimension of elliptic spaces. Some results in some simple cases
• The conjecture H: A lower bound of cohomologic dimension for an elliptic space