The conjecture H: A lower bound of cohomologic dimension for an elliptic space

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The goal of this paper is to ameliorate the sufficients conditions, already established by the first author so that the sum of the numbers of Betti, of 1-connected rational finite CW-complex, is higher than the dimension of his $\mathbb Q$-vectorial space of homotopy, we will present it in two aspects, one algebraic and another geometrical.
18 pages; Work exposed by the second author in the Algebraic topology conference of Angers, France, October 2007

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