Abstract
For $k \geq 2$, let $M^{4k-1}$ be a closed $(2k-2)$-connected 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 $M \sharp \Sigma$ admits a Ricci positive metric. This follows from a new description of these manifolds as the boundaries of explicit plumbings.
Citation
Diarmuid Crowley. David J. Wraith. "Positive Ricci curvature on highly connected manifolds." J. Differential Geom. 106 (2) 187 - 243, June 2017. https://doi.org/10.4310/jdg/1497405625