The loop space homotopy type of simply-connected four-manifolds and their generalizations (Q2251887)

In this paper, the authors determine the homotopy decomposition of loop spaces of simply connected four dimensional manifolds, \((n-1)\)-connected \(2n\) dimensional manifolds \((n\notin\{4,8\}\)) and connected sums of product of spheres. These homotopy decompositions are obtained as the special cases of a more general loop space decomposition of certain torsion-free CW complexes. The proof is based on elementary homotopy theory.