Generalized Surgery on Riemannian Manifolds of Positive Ricci Curvature

Abstract: The surgery theorem of Wraith states that positive Ricci curvature is preserved under surgery if certain metric and dimensional conditions are satisfied. We generalize this theorem as follows: Instead of attaching a product of a sphere and a disc, we glue a sphere bundle over a manifold with a so-called core metric, a type of metric which was recently introduced by Burdick to construct metrics of positive Ricci curvature on connected sums. As applications we construct core metrics on 2-sphere bundles, where the base admits a core metric, and obtain new examples of 6-manifolds with metrics of positive Ricci curvature.