Work

Non-geometric veering triangulations

Year: 2014

Type: preprint

Abstract: Recently, Ian Agol introduced a class of "veering" ideal triangulations for mapping tori of pseudo-Anosov homeomorphisms of surfaces punctured along the singular points. These triangulations have very special combinatorial properties, and Agol asked if these are "geometric", i.e. realised in the complete hyperbolic metric with all tetrahedra positively oriented. This paper describes a computer program Veering, building on the program Trains by Toby Hall, for generating these triangulations starting from a description of the homeomorphism as a product of Dehn twists. Using this we obtain the first examples of non-geometric veering triangulations; the smallest example we have found is a triangulation with 13 tetrahedra.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1406.6439

Authors: Hodgson, Craig D., Issa, Ahmad, Segerman, Henry

Institutions: The University of Melbourne, The University of Texas at Austin, Oklahoma State University

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W2950966948

Cites: 10

Cited by:

Related to: 20