The polyhedral decomposition of cusped hyperbolic $n$-manifolds with totally geodesic boundary
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909315044999168 |
|---|---|
| author | Huabin, Ge Longsong, Jia Faze, Zhang |
| author_facet | Huabin, Ge Longsong, Jia Faze, Zhang |
| contents | Let $M$ be a volume finite non-compact complete hyperbolic $n$-manifold with totally geodesic boundary. We show that there exists a polyhedral decomposition of $M$ such that each cell is either an ideal polyhedron or a partially truncated polyhedron with exactly one truncated face. This result parallels Epstein-Penner's ideal decomposition \cite{EP} for cusped hyperbolic manifolds and Kojima's truncated polyhedron decomposition \cite{Kojima} for compact hyperbolic manifolds with totally geodesic boundary. We take two different approaches to demonstrate the main result in this paper. We also show that the number of polyhedral decompositions of $M$ is finite. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_08923 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The polyhedral decomposition of cusped hyperbolic $n$-manifolds with totally geodesic boundary Huabin, Ge Longsong, Jia Faze, Zhang Geometric Topology Differential Geometry 57M50, 57Q15 Let $M$ be a volume finite non-compact complete hyperbolic $n$-manifold with totally geodesic boundary. We show that there exists a polyhedral decomposition of $M$ such that each cell is either an ideal polyhedron or a partially truncated polyhedron with exactly one truncated face. This result parallels Epstein-Penner's ideal decomposition \cite{EP} for cusped hyperbolic manifolds and Kojima's truncated polyhedron decomposition \cite{Kojima} for compact hyperbolic manifolds with totally geodesic boundary. We take two different approaches to demonstrate the main result in this paper. We also show that the number of polyhedral decompositions of $M$ is finite. |
| title | The polyhedral decomposition of cusped hyperbolic $n$-manifolds with totally geodesic boundary |
| topic | Geometric Topology Differential Geometry 57M50, 57Q15 |
| url | https://arxiv.org/abs/2409.08923 |