Almost non-negatively curved 4-manifolds with torus symmetry

John Harvey; Catherine Searle

doi:10.1090/proc/15093

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arXiv · 1907.06702

Almost non-negatively curved 4-manifolds with torus symmetry

John Harvey·Catherine Searle

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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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John Harvey, Catherine Searle. 2019-07-15. Almost non-negatively curved 4-manifolds with torus symmetry. https://doi.org/10.1090/proc/15093

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