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 4manifold 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.
Fields of Study & Subjects
Geometric and Algebraic Topology
Mathematical Dynamics and Fractals
Homotopy and Cohomology in Algebraic Topology
Publication details
- Journal / source
- Algebraic & Geometric Topology
- Volume
- 26
- Issue
- 3
- Pages
- 1077–1093
- Publication date
- 1 April 2026
- Language
- EN