Generalized Surgery on Riemannian Manifolds of Positive Ricci Curvature

The surgery theorem of Wraith states that the existence of metrics of positive Ricci curvature is preserved under surgery if certain metric and dimensional conditions are satisfied. We generalize this theorem by relaxing the conditions on the dimensions involved and by generalizing the surgery construction itself. As applications we construct metrics of positive Ricci curvature on manifolds obtained by plumbing. Specifically, this construction provides an extension of a result of Burdick on the existence of metrics of positive Ricci curvature on connected sums of linear sphere bundles, and, moreover, it yields infinite families of new examples of manifolds with a metric of positive Ricci curvature in all dimensions divisible by 6.