Generalized surgery on Riemannian manifolds of positive Ricci curvature

Reiser, Philipp

doi:10.1090/tran/8789

Generalized surgery on Riemannian manifolds of positive Ricci curvature
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by Philipp Reiser;

Trans. Amer. Math. Soc. 376 (2023), 3397-3418

DOI: https://doi.org/10.1090/tran/8789

Published electronically: February 9, 2023

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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 extend a result of Burdick on the existence of core metrics on certain sphere bundles and obtain new examples of 6-manifolds with metrics of positive Ricci curvature.

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