English

Random veering triangulations are not geometric

Geometric Topology 2020-11-26 v2

Abstract

Every pseudo-Anosov mapping class φ\varphi defines an associated veering triangulation τφ\tau_\varphi of a punctured mapping torus. We show that generically, τφ\tau_\varphi is not geometric. Here, the word "generic" can be taken either with respect to random walks in mapping class groups or with respect to counting geodesics in moduli space. Tools in the proof include Teichm\"uller theory, the Ending Lamination Theorem, study of the Thurston norm, and rigorous computation.

Keywords

Cite

@article{arxiv.1808.05586,
  title  = {Random veering triangulations are not geometric},
  author = {David Futer and Samuel J. Taylor and William Worden},
  journal= {arXiv preprint arXiv:1808.05586},
  year   = {2020}
}

Comments

38 pages, 9 figures. To appear in Groups, Geometry, and Dynamics

R2 v1 2026-06-23T03:36:05.126Z