A generalization of the Perelman gluing theorem and applications

2023/08/14 by Philipp Reiser, Reiser, Philipp, David J. Wraith +1 · 3 citations
Mathematics · Physics and Astronomy · #53C20 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2308.06996

openalex publication_date 2023/08/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We extend a positive Ricci curvature gluing theorem of Perelman to a range of positive intermediate curvature conditions, ranging from positive scalar curvature up to (and including) positive sectional curvature. As an application of this, we demonstrate that the observer moduli space of metrics with positive intermediate Ricci curvatures can have non-trivial higher homotopy groups. Further applications include deriving a sufficient condition for the existence of a metric with positive intermediate Ricci curvature and totally geodesic boundary.

Cited by

• Scalar Curvature in Dimension 4
• Positive intermediate Ricci curvature on cohomogeneity one manifolds in low dimensions
• On Hopf's conjecture and positive second intermediate Ricci curvature

Related

• Positive intermediate Ricci curvature on products of homogeneous spaces
• Positive intermediate curvatures and Ricci flow
• Metrics of positive Ricci curvature on vector bundles over nilmanifolds
• Moduli Spaces of Positive Curvature Metrics in Dimension Four and Beyond
• Constrained deformations of positive scalar curvature metrics