Cusp-transitive 4-manifolds with every cusp section
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.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2024
- DOI:
- 10.48550/arXiv.2408.05080
- arXiv:
- arXiv:2408.05080
- Bibcode:
- 2024arXiv240805080G
- Keywords:
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- Mathematics - Geometric Topology;
- 57M50
- E-Print:
- 18 pages, 7 figures. Added acknowledgments