Positive intermediate Ricci curvature on connected sums

Reiser, Philipp; Wraith, David J

doi:10.2140/agt.2025.25.4209

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Positive intermediate Ricci curvature on connected sums

Philipp Reiser and David J Wraith

Algebraic & Geometric Topology 25 (2025) 4209–4227

DOI: 10.2140/agt.2025.25.4209

Abstract

We consider the problem of performing connected sums in the context of positive $k^{th}$ -intermediate Ricci curvature. We show that such connected sums are possible if the manifolds involved possess “ $k$ -core metrics” for some $k$ . Here, a $k$ -core metric is a generalisation of the notion of core metric introduced by Burdick for positive Ricci curvature. Further, we show that connected sums of linear sphere bundles over bases admitting such metrics admit positive $k^{th}$ -intermediate Ricci curvature for $k$ in a particular range. This follows from a plumbing result we establish, which generalises other recent plumbing results in the literature and is possibly of independent interest. As an example of a manifold admitting a $k$ -core metric, we prove that $ℍ P^{n}$ admits a $(4 n - 3)$ -core metric and that $𝕆 P^{2}$ admits a $9$ -core metric, and we show that in both cases these are optimal.

Keywords

connected sum, intermediate Ricci curvature, plumbing

Mathematical Subject Classification

Primary: 53C20

References

Publication

Received: 25 January 2024

Revised: 15 August 2024

Accepted: 24 November 2024

Published: 29 October 2025

Authors

Philipp Reiser
Department of Mathematics University of Fribourg Fribourg Switzerland

David J Wraith
Department of Mathematics and Statistics Maynooth University Maynooth Ireland

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Volume 25, issue 7 (2025)