Open Access
June 2017 Positive Ricci curvature on highly connected manifolds
Diarmuid Crowley, David J. Wraith
J. Differential Geom. 106(2): 187-243 (June 2017). DOI: 10.4310/jdg/1497405625


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.


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Diarmuid Crowley. David J. Wraith. "Positive Ricci curvature on highly connected manifolds." J. Differential Geom. 106 (2) 187 - 243, June 2017.


Received: 11 February 2015; Published: June 2017
First available in Project Euclid: 14 June 2017

zbMATH: 06846950
MathSciNet: MR3662991
Digital Object Identifier: 10.4310/jdg/1497405625

Rights: Copyright © 2017 Lehigh University

Vol.106 • No. 2 • June 2017
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