On the Hilali Conjecture for Configuration Spaces of Closed Manifolds

Abstract

The first author conjectured in 1990 (see [18]) that for any simply-connected elliptic space, the total dimension of the rational homotopy does not exceed that of its rational cohomology. Our main purpose in this paper is to investigate the following: does the Hilali conjecture holds for the configuration spaces of a rationally elliptic and simply connected topological space when it already holds for the space itself. We will prove that this statement is true for closed manifolds.