Parallelizability of finite H-spaces (Q1070571)

There is little in the literature on the connection between manifolds and finite H-spaces. One suspects two reasons for this: the beliefs that everything will be obvious to W. Browder and that no useful information will be gained about (the homotopy theory of) H-spaces. The authors prove that with hypotheses on the mod 2 homotopy type and the fundamental group, a finite H-space has the homotopy type of a closed parallelizable smooth manifold. Further results on the geometry of H-spaces are promised.