Gaps in the Milnor–Moore spectral sequence and the Hilali conjecture

Abstract

Let X be a simply-connected space, $$(\Lambda V, d)$$ its minimal Sullivan model and $$d_k$$ ( $$k\ge 2$$ ) the first non-zero homogeneous part of the differential d. In this paper, assuming that $$(\Lambda V, d_k)$$ is elliptic, we show that $$H(\Lambda V,d)$$ has no $$e_0$$ -gap and consequently we confirm the Hilali conjecture when $$V = V^{odd}$$ or else when $$k\ge 3$$ .