An inverse to the Poincaré conjecture

The notion of Poincaré manifolds is introduced, which are roughly 1-connected manifolds which are determined by tem heir homology. The Poincaré conjecture says that spheres are Poincaré manifolds. The determination of all Poincaré manifolds is a sort of inverse to the Poincaré conjecture. Besides some information in low dimensions we give some results on generalized Poincaré manifolds.