## Journal of Differential Geometry

### Positive Ricci curvature on highly connected manifolds

#### 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.

#### Article information

Source
J. Differential Geom., Volume 106, Number 2 (2017), 187-243.

Dates
First available in Project Euclid: 14 June 2017

https://projecteuclid.org/euclid.jdg/1497405625

Digital Object Identifier
doi:10.4310/jdg/1497405625

Mathematical Reviews number (MathSciNet)
MR3662991

Zentralblatt MATH identifier
06846950

#### Citation

Crowley, Diarmuid; Wraith, David J. Positive Ricci curvature on highly connected manifolds. J. Differential Geom. 106 (2017), no. 2, 187--243. doi:10.4310/jdg/1497405625. https://projecteuclid.org/euclid.jdg/1497405625