Positive Ricci curvature on highly connected manifolds

Abstract

For $k\ge 2,$ let $M^{4k-1}$ be a $(2k-2)$-connected closed manifold. If $k\equiv 1$ mod $4$ assume further that $M$ is $(2k-1)$-parallelisable. Then there is a homotopy sphere ${\Sigma }^{4k-1}$ such that $M♯\Sigma$ admits a Ricci positive metric. This follows from a new description of these manifolds as the boundaries of explicit plumbings.

Corrected some minor typos and changed document class to amsart. The new document class added 10 pages, so the paper is now now 46 pages