First Betti number and collapse

2022/09/26 by Sergio Zamora, Zamora, Sergio · 1 citation
Computer Science · Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Metric Geometry (math.MG) #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2209.12628

openalex publication_date 2022/09/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that when a sequence of Riemannian manifolds collapses under a lower Ricci curvature bound, the first Betti number cannot drop more than the dimension.

Cited by

• Instability of the fundamental group for non-collapsed Ricci-limits

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