Positive Ricci Curvature on Twisted Suspensions
DOKPE
- Reiser, Philipp ORCID University of Fribourg
- 2024
Published in:
- International Mathematics Research Notices. - Oxford, UK : Oxford University Press. - 2024, no. 22, p. 14115–14137
English
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.
- Faculty
- Faculté des sciences et de médecine
- Department
- Département de Mathématiques
- Language
-
- English
- Classification
- Mathematics
- License
- CC BY
- Open access status
- hybrid
- Identifiers
-
- DOI 10.1093/imrn/rnae231
- ISSN 1073-7928
- ISSN 1687-0247
- Persistent URL
- https://folia.unifr.ch/unifr/documents/330422
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