L'Application Canonique $J:H^2(X) \otimes H^2(X)->H^1(X\otimes X)$ n'est pas Surjective en Général

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We introduce the $H^1$-projective property, and use it to construct a Banach space $X$ such that the natural map $J:H^2(X)\otimes H^2(X) -> H^1(X\otimes X)$ is not onto.
9 pages, French with abridged english version

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