Philipp Reiser, Karlsruhe Institute of Technology

Title: 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.
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.