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arXiv · 2103.05517

Generalized Surgery on Riemannian Manifolds of Positive Ricci Curvature

Philipp Reiser
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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.

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Philipp Reiser. 2021-03-09. Generalized Surgery on Riemannian Manifolds of Positive Ricci Curvature. https://doi.org/10.1090/tran/8789

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