Positive Ricci curvature on highly connected manifolds

Diarmuid Crowley, David J. Wraith

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 sphe…