Positive Ricci Curvature on Highly Connected Manifolds

Diarmuid Crowley, David J. Wraith

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)


For k ≥ 2, let M4k−1 be a closed (2k−2)-connected manifold. If k ≡ 1 mod 4 assume further that M is (2k−1)-parallelisable. Then there is a homotopy sphere Σ4k−1 such that M ]Σ admits a Ricci positive metric. This follows from a new description of these manifolds as the boundaries of explicit plumbings.
Original languageEnglish
Pages (from-to)187-243
Number of pages57
JournalJournal of Differential Geometry
Issue number2
Early online date14 Jun 2017
Publication statusPublished - Jun 2017

Bibliographical note

Acknowledgments. We would like to thank Jim Davis, Anand Dessai,
Karsten Grove, Matthias Kreck, Gabriele Nebe, Walter Neumann,
Andrew Ranicki, Andras Stipsicz and Stephan Stolz for various helpful
comments. The first author would like to thank the National University
of Ireland Maynooth for its hospitality during the 2013 Irish Geometry
Conference, which directly supported research for this paper. The first
author acknowledges the support of the Leibniz Prize of Wolfgang Luck,
granted by the Deutsche Forschungsgemeinschaft.


Dive into the research topics of 'Positive Ricci Curvature on Highly Connected Manifolds'. Together they form a unique fingerprint.

Cite this