preserved under surgery if certain metric and dimensional conditions are satisfied.

In this talk I will present a generalization of this theorem: 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.

This generalization leads to new examples of manifolds
with core metrics and

manifolds with positive Ricci curvature. As
applications I will show how to

construct core metrics on 2-sphere
bundles and present some concrete examples

in dimension 6.