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This is a Quantitative Study study.

October 13, 2025Open Access

Some closed hyperbolic 5-manifolds

Key Points

Explicit construction yields a family of closed arithmetic hyperbolic 5-manifolds, showing rich geometric properties.
The study includes the volume and first Betti number, which characterize these manifolds further, providing essential insights.
A related family of 5-manifolds is explored, presenting a larger volume with a simpler structure than previously constructed ones.
Findings refine our understanding of hyperbolic geometry and its various manifestations, opening doors for future research.

Abstract

We give an explicit construction of a family of closed arithmetic hyperbolic 5-manifolds, tessellated by 117 964 800 = 512 16 14400 copies of a Coxeter simplicial prism. We proceed to study various properties of these manifolds, such as the volume and the first Betti number. We also describe a related family of 5-manifolds with a larger volume, but a simpler construction.

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Cite This Study

Jacopo G. Chen (Wed,) studied this question.

synapsesocial.com/papers/68ecc715d1cc7436f7d1886a https://doi.org/https://doi.org/10.48550/arxiv.2502.19225

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