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Parallelizability of finite H-spaces. (English) Zbl 0585.55006

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.
Reviewer: Y.Hubbuck

MSC:

55P45 \(H\)-spaces and duals
57R67 Surgery obstructions, Wall groups
55R05 Fiber spaces in algebraic topology
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