First Betti number and collapse

Sergio Zamora

First Betti number and collapse

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arxiv 2209.12628 v1 pith:HMNW7MKT submitted 2022-09-26 math.DG math.MG

Sergio Zamora This is my paper · ORCID

classification math.DGmath.MG

keywords bettifirstnumberboundcannotcollapsecollapsescurvature

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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.

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Instability of the fundamental group for non-collapsed Ricci-limits
math.DG 2025-05 conditional novelty 7.0 of 10

There exist two sequences of closed 4-manifolds with nonnegative Ricci curvature, bounded diameter and volume, which converge to the same Gromov-Hausdorff limit yet have fundamental groups Z/2Z and trivial.

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