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.