Homotopy groups of certain highly connected manifolds via loop space homology

For n >= 2 we consider (n - 1)-connected closed manifolds of dimension at most (3n - 2). We prove that away from a finite set of primes, the p-local homotopy groups of M are determined by the dimension of the space of indecomposable elements in the cohomology ring H*(M; Q). Moreover, we show that these p-local homotopy groups can be expressed as a direct sum of p-local homotopy groups of spheres. This generalizes some of the results of our earlier work [1].