  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.
