Cusp-transitive 4-manifolds with every cusp section

Chen, Jacopo Guoyi; Rizzi, Edoardo

doi:10.2140/agt.2026.26.1077

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ISSN (electronic): 1472-2739

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Cusp-transitive $4$-manifolds with every cusp section

Jacopo Guoyi Chen and Edoardo Rizzi

Algebraic & Geometric Topology 26 (2026) 1077–1093

DOI: 10.2140/agt.2026.26.1077

Abstract

We realize every closed flat 3-manifold as a cusp section of a complete, finite-volume hyperbolic 4-manifold whose symmetry group acts transitively on the set of cusps. Moreover, for every such 3-manifold, a dense subset of its flat metrics can be realized as cusp sections of a cusp-transitive 4-manifold. Finally, we prove that there are many 4-manifolds with pairwise isometric cusps for any given cusp type.

Keywords

cusp-transitive manifolds, Coxeter polytopes, hyperbolic manifolds, space of flat metrics

Mathematical Subject Classification

Primary: 57M50

References

Publication

Received: 12 August 2024

Revised: 10 December 2024

Accepted: 10 February 2025

Published: 1 April 2026

Authors

Jacopo Guoyi Chen
Scuola Normale Superiore Pisa Italy

Edoardo Rizzi
Scuola Normale Superiore Pisa Italy

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Volume 26, issue 3 (2026)