Which H-spaces are manifolds? I
The authors are concerned with the question whether a finite dimensional H-space is of the homotopy type of a closed manifold. This is a question first formulated and studied by W. Browder, who showed that the answer is positive when X is simply connected. In this article, the authors show that the answer is also positive when the fundamental group \(\pi_ 1(X,*)\) is either an odd p-group or infinite with at most cyclic 2- torsion. They also study the case when \(\pi_ 1(X,*)\) has only 2- torsion, and they give examples, when \(\pi_ 1(X,*)\cong {\mathbb{Z}}_ 2\times {\mathbb{Z}}_ 2\), of Poincaré complexes X not homotopy equivalent to closed manifolds.
scientific article; zbMATH DE number 4121043