Work

Random veering triangulations are not geometric

Year: 2020

Type: article

Abstract: Every pseudo-Anosov mapping class \phi defines an associated veering triangulation \tau_\phi of a punctured mapping torus. We show that generically, \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.

Source: Groups Geometry and Dynamics

DOI: 10.4171/ggd/575

Authors: David Futer, Samuel J. Taylor, William Worden

Institutions: Rice University, Temple University

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Awards: PostDoctoral Research Fellowship, Connections in low-dimensional topology, Hyperbolic Manifolds and Their Groups, Negative Curvature in Fiber Bundles and Counting Problems