PreprintCC BY 4.0arXiv
Geometric ideal triangulations of hyperbolic 3-manifolds
Abstract
We resolve the longstanding geometric ideal triangulation conjecture arising from Thurston's theory of hyperbolic 3-manifolds: every finite-volume cusped hyperbolic 3-manifold admits a finite geometric ideal triangulation realizing its complete hyperbolic structure.
Related
- Local Combinatorial Criteria for Geometric Hyper-ideal Triangulations via Combinatorial Ricci Flow
- Non-geometric ideal triangulations with all edge valences at least six
- Three-manifolds that do not admit veering triangulations
- Loop content of bond percolation on hyperbolic triangulations: an exact identity and a 1/λ expansion
- A note on right-angled, ideal hyperbolic polyhedra
BibTeX
@misc{ge2026geometric,
title = {{Geometric ideal triangulations of hyperbolic 3-manifolds}},
author = {Huabin Ge},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.27635},
eprint = {2609.27635},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.27635},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Geometric ideal triangulations of hyperbolic 3-manifolds
AU - Huabin Ge
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.27635
UR - https://arxiv.org/abs/2609.27635
AB - We resolve the longstanding geometric ideal triangulation conjecture arising from Thurston's theory of hyperbolic 3-manifolds: every finite-volume cusped hyperbolic 3-manifold admits a finite geometric ideal triangulation realizing its complete hyperbolic structure.
ER -