Positive Ricci curvature on highly connected manifolds

Abstract

For k ≥ 2, let M4k-1 be a closed (2k-2)-connected manifold. If k = 1 mod 4 assume further that M is (2k-l)-parallelisable. Then there is a homotopy sphere Σ4k-1 such that M#Σ admits a Ricci positive metric. This follows from a new description of these manifolds as the boundaries of explicit plumbings.