On the topology of the moduli space of positive scalar curvature concordances

2024/07/30 by Boris Botvinnik, Botvinnik, Boris, David J. Wraith +1
Mathematics · Physics and Astronomy · #53C20 #Advanced Banach Space Theory #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2407.21218

openalex publication_date 2024/07/30 · openalex created_date 2024/08/04 · openalex updated_date 2026/07/28

Abstract

Let M be a manifold which admits a metric with positive scalar curvature (or a positive intermediate curvature in a suitable sense). We study the moduli space \mathscrM^pos_*_\sqcup(M× I)_g of concordances of such metrics (with appropriate boundary conditions) which restrict to a given metric g on M × \0\ ∪∂ M × I. We show that π_4*\mathscrM^pos_*_\sqcup(M × I)_g ⊗ \mathbb Q ≠ 0 in a stable range provided dim M is even. We obtain analogous results when positive scalar curvature is replaced by k-positive Ricci curvature for k ≥ 2.

Related

• Metrics of positive scalar curvature and generalised Morse functions, part 1
• Concordances in Positive Scalar Curvature and Index Theory
• On the homotopy type of the space R⁺(M)
• Moduli Spaces of Positive Curvature Metrics in Dimension Four and Beyond
• A generalization of Geroch's conjecture