On a Conjecture of Yamaguchi and Yokura

Let be a fibration of simply connected elliptic spaces. Our paper investigates the conjecture proposed by T. Yamaguchi and S. Yokura, states that dim Ker dim Ker . Our goal is to prove this conjecture when and satisfy the condition . We go also on to establish a well-known conjecture of Hilali for a class of spaces which puts it into the context of fibration