Skip to content
DraconiticResearch
Search Sources API
197,768 studies31 sourcesUpdated 44 min ago
PreprintarXiv licencearXiv

Three-manifolds that do not admit veering triangulations

  • Layne Hall
Open at sourcePDFDOICite

Abstract

We show that if a three-manifold M admits a veering triangulation, then the dual spine of every essential triangulation of M can be smoothed to a branched surface. We use this criterion to identify a large collection of cusped hyperbolic three-manifolds that do not admit veering triangulations. We then use the same criterion to construct the first infinite family of cusped hyperbolic three-manifolds without veering triangulations.

Related

  1. Veering triangulations of once-punctured torus bundles are unique
    Saul Schleimer, Henry Segerman
    arXivPreprintCC0Full textGeometry & topologyarXiv
  2. From veering triangulations to convergence actions and back again
    Jason Fox Manning, Saul Schleimer, Henry Segerman
    arXivPreprintCC0Full textGeometry & topologyarXiv
  3. Drilling veering triangulations with applications to pseudo-Anosov flows
    Anna Parlak, Henry Segerman
    arXivPreprintarXiv licenceFull textDynamical systemsGeometry & topologyarXiv
  4. Geometric ideal triangulations of hyperbolic 3-manifolds
    Huabin Ge
    arXivPreprintCC BY 4.0Full textGeometry & topologyarXiv
  5. Infinitely many graph manifolds with unique geometrical piece that admit arbitrarily many Anosov flows
    O. Pochinka, V. Shmukler
    arXivPreprintCC BY 4.0Full textDynamical systemsarXiv

Cite

BibTeXRIS
BibTeX
@misc{hall2026threemanifolds,
  title = {{Three-manifolds that do not admit veering triangulations}},
  author = {Layne Hall},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.37057},
  eprint = {2610.37057},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.37057},
}
RIS
TY  - UNPB
TI  - Three-manifolds that do not admit veering triangulations
AU  - Layne Hall
PY  - 2026
DA  - 2026/10/27
PB  - arXiv
DO  - 10.48550/arxiv.2610.37057
UR  - https://arxiv.org/abs/2610.37057
AB  - We show that if a three-manifold M admits a veering triangulation, then the dual spine of every essential triangulation of M can be smoothed to a branched surface. We use this criterion to identify a large collection of cusped hyperbolic three-manifolds that do not admit veering triangulations. We then use the same criterion to construct the first infinite family of cusped hyperbolic three-manifolds without veering triangulations.
ER  -