Cusp-transitive 4-manifolds with every cusp section

Jacopo Guoyi Chen; Edoardo Rizzi

doi:10.2140/agt.2026.26.1077

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arXiv · 2408.05080

Cusp-transitive 4-manifolds with every cusp section

Jacopo Guoyi Chen·Edoardo Rizzi

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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 a lot of 4-manifolds with pairwise isometric cusps, for any given cusp type.

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BibTeX RIS

Jacopo Guoyi Chen, Edoardo Rizzi. 2024-08-09. Cusp-transitive 4-manifolds with every cusp section. https://doi.org/10.2140/agt.2026.26.1077

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