Almost non-negatively curved 4-manifolds with torus symmetry

Harvey, John; Searle, Catherine

doi:10.1090/proc/15093

Almost non-negatively curved $4$-manifolds with torus symmetry
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by John Harvey and Catherine Searle

Proc. Amer. Math. Soc. 148 (2020), 4933-4950

DOI: https://doi.org/10.1090/proc/15093

Published electronically: August 14, 2020

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Abstract:

We prove that if a closed, smooth, simply-connected 4-manifold with a circle action admits an almost non-negatively curved sequence of invariant Riemannian metrics, then it also admits a non-negatively curved Riemannian metric invariant with respect to the same action. The same is shown for torus actions of higher rank, giving a classification of closed, smooth, simply-connected 4-manifolds of almost non-negative curvature under the assumption of torus symmetry.

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