On 3-connected finite H-spaces (Q1060736)

This paper deals with a classification problem of finite H-spaces. Its main results are: Theorem 1.4: If X is a 3-connected finite H-space satisfying: (1) The rational and the mod 2 cohomology Hopf algebras of X are primitively generated, (2) There is no generator of dim 15 in the mod 2 cohomology of X, then X has the homotopy type of a product of 7 dim spheres. - One of the outcomes of this paper (not mentioned in the text) is the elimination of one of the few unsettled cases of the realization problem of polynomial algebras as cohomology of spaces. The proof uses methods similar to the classical ones of Browder and of Thomas and K- theory arguments similar to Hubbucks's.