Positive intermediate Ricci curvature on connected sums

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 HP n admits a .4n3/-core metric and that OP 2 admits a 9-core metric, and we show that in both cases these are optimal.53C20