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.