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Constructing manifolds by homotopy equivalences I. An obstruction to constructing PL-manifolds from homology manifolds

Hajime Sato (1972)

Annales de l'institut Fourier

We aim at constructing a PL-manifold which is cellularly equivalent to a given homology manifold M n . The main theorem says that there is a unique obstruction element in H n - 4 ( M , 3 ) , where 3 is the group of 3-dimensional PL-homology spheres modulo those which are the boundary of an acyclic PL-manifold. If the obstruction is zero and M is compact, we obtain a PL-manifold which is simple homotopy equivalent to M .

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