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International Mathematics Research Notices
Article . 2024 . Peer-reviewed
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Article . 2024
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Positive Ricci Curvature on Twisted Suspensions

Positive Ricci curvature on twisted suspensions
Authors: Reiser, Philipp;

Positive Ricci Curvature on Twisted Suspensions

Abstract

Abstract The twisted suspension of a manifold is obtained by surgery along the fibre of a principal circle bundle over the manifold. It generalizes the spinning operation for knots and preserves various topological properties. In this article, we show that Riemannian metrics of positive Ricci curvature can be lifted along twisted suspensions. As an application we show that the maximal symmetry rank of a closed, simply connected Riemannian manifold of positive Ricci curvature is $(n-2)$ in all dimensions $n\geq 4$. Further applications include simply connected 6-manifolds whose homology has torsion, (rational) homology spheres in all dimensions at least 4, and manifolds with prescribed third homology.

Country
Switzerland
Related Organizations
Keywords

positive Ricci curvature, Mathematics - Differential Geometry, Mathematics - Geometric Topology, Differential Geometry (math.DG), FOS: Mathematics, suspension, Geometric Topology (math.GT), 53C20, 57R65, 57S15, Global Riemannian geometry, including pinching, twisted suspension

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
1
Average
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