PreprintCC0arXiv
Veering triangulations of once-punctured torus bundles are unique
Abstract
We show that each hyperbolic once-punctured torus bundle has exactly one veering triangulation. We also find manifolds for which the exact number of veering structures is known and is greater than one. Finally, we give new examples of manifolds without veering triangulations.
Related
- Three-manifolds that do not admit veering triangulations
- From veering triangulations to convergence actions and back again
- Drilling veering triangulations with applications to pseudo-Anosov flows
- Exact curve counting of given word length on the once-punctured torus
- Torus knots as loop-edges in three-sphere triangulations
BibTeX
@misc{schleimer2026veering,
title = {{Veering triangulations of once-punctured torus bundles are unique}},
author = {Saul Schleimer and Henry Segerman},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.32771},
eprint = {2610.32771},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.32771},
note = {CC0},
}
RIS
TY - UNPB
TI - Veering triangulations of once-punctured torus bundles are unique
AU - Saul Schleimer
AU - Henry Segerman
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.32771
UR - https://arxiv.org/abs/2610.32771
AB - We show that each hyperbolic once-punctured torus bundle has exactly one veering triangulation. We also find manifolds for which the exact number of veering structures is known and is greater than one. Finally, we give new examples of manifolds without veering triangulations.
ER -