Random veering triangulations are not geometric
| Autor: | William Worden, David Futer, Samuel J. Taylor |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
57M50 (primary) 57Q15
30F30 30F40 60G50 (secondary) Class (set theory) Pure mathematics Mathematics::Dynamical Systems Geodesic Computation 010102 general mathematics Triangulation (social science) Geometric Topology (math.GT) 16. Peace & justice Random walk 01 natural sciences Mathematics::Geometric Topology Moduli space Mathematics - Geometric Topology 0103 physical sciences FOS: Mathematics Mapping torus Discrete Mathematics and Combinatorics 010307 mathematical physics Geometry and Topology 0101 mathematics Word (group theory) Mathematics |
| Popis: | Every pseudo-Anosov mapping class $\varphi$ defines an associated veering triangulation $\tau_\varphi$ of a punctured mapping torus. We show that generically, $\tau_\varphi$ 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. Comment: 38 pages, 9 figures. To appear in Groups, Geometry, and Dynamics |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|