Sergio Zamora

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20182021

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math.DG2022★ 1 cited

First Betti number and collapse

Sergio Zamora

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.

math.DG2021

Fundamental groups of aspherical manifolds that collapse

Sergio Zamora

We show that if a sequence $M_{n}$ of closed aspherical $d$ -dimensional Riemannian manifolds with Ricci curvature uniformly bounded below and diameter uniformly bounded above collaps…

math.DG2020

Tori Can't Collapse to an Interval

Sergio Zamora

Here we prove that under a lower sectional curvature bound, a sequence of Riemannian manifolds diffeomorphic to the standard $m$ -dimensional torus cannot converge in the Gromov--Ha…