The loop space homotopy type of simply-connected four-manifolds and their generalizations

We determine loop space decompositions of simply-connected four-manifolds, (n−1)(n−1)-connected 2n  -dimensional manifolds provided n∉{4,8}n∉{4,8}, and connected sums of products of two spheres. These are obtained as special cases of a more general loop space decomposition of certain torsion-free CW-complexes with well-behaved skeleta and some Poincaré duality features.