JournalsggdVol. 14, No. 3pp. 1077–1126

Random veering triangulations are not geometric

  • David Futer

    Temple University, Philadelphia, USA
  • Samuel J. Taylor

    Temple University, Philadelphia, USA
  • William Worden

    Rice University, Houston, USA
Random veering triangulations are not geometric cover
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Abstract

Every pseudo-Anosov mapping class ϕ\phi defines an associated veering triangulation τϕ\tau_\phi of a punctured mapping torus. We show that generically, τϕ\tau_\phi 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 Teichmüller theory, the Ending Lamination Theorem, study of the Thurston norm, and rigorous computation.

Cite this article

David Futer, Samuel J. Taylor, William Worden, Random veering triangulations are not geometric. Groups Geom. Dyn. 14 (2020), no. 3, pp. 1077–1126

DOI 10.4171/GGD/575