Work

Positive Ricci Curvature on Twisted Suspensions

Year: 2024

Type: article

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.

Source: International Mathematics Research Notices

DOI: 10.1093/imrn/rnae231

Author: Philipp Reiser

Institution: University of Fribourg

Language: English

Topic: Advanced Differential Geometry Research

Subfield: Astronomy and Astrophysics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $4,534

Funders: California Department of Fish and Game, Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung