Torus covers with controlled volume and diameter

We show that under a lower Ricci curvature bound and an upper diameter bound, a torus admits a finite-sheeted covering space with volume bounded from below and diameter bounded from above. This partially recovers a result of Kloeckner and Sabourau [J. Topol. Anal. 12 (2020), pp. 713–734], whose original proof contains a serious gap that currently lacks a resolution.

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Publication Details

Journal
Proceedings of the American Mathematical Society
Published
2025-11-25
DOI
https://doi.org/10.1090/proc/17473
Primary Topic
Geometric and Algebraic Topology
Type
article
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article

Torus covers with controlled volume and diameter

Sergio Zamora
Proceedings of the American Mathematical Society
Geometric and Algebraic Topology
article

Torus covers with controlled volume and diameter

Sergio Zamora
article en

Abstract

We show that under a lower Ricci curvature bound and an upper diameter bound, a torus admits a finite-sheeted covering space with volume bounded from below and diameter bounded from above. This partially recovers a result of Kloeckner and Sabourau [J. Topol. Anal. 12 (2020), pp. 713–734], whose original proof contains a serious gap that currently lacks a resolution.

Proceedings of the American Mathematical SocietyVol. 154(2)
Oregon State University (US)
Openalex Percentile: Top 58%
Geometric and Algebraic Topology
DOISourceOpenAlex
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Torus covers with controlled volume and diameter — Sergio Zamora · Proceedings of the American Mathematical Society (2025) | TGRS Research Map | TGRS