Explicit angle structures for veering triangulations

TL;DR

This paper proves that all veering triangulations admit positive angle structures, providing explicit bounds on angles and insights into boundary holonomy, thus advancing understanding of hyperbolic 3-manifold triangulations.

Contribution

It offers a constructive proof that every veering triangulation admits positive angle structures, including explicit bounds and boundary holonomy information.

Findings

All veering triangulations admit positive angle structures.

Explicit lower bounds on the smallest angles are provided.

Information about the angled holonomy of boundary tori is obtained.

Abstract

Agol recently introduced the notion of a veering triangulation, and showed that such triangulations naturally arise as layered triangulations of fibered hyperbolic 3-manifolds. We prove, by a constructive argument, that every veering triangulation admits positive angle structures, recovering a result of Hodgson, Rubinstein, Segerman, and Tillmann. Our construction leads to explicit lower bounds on the smallest angle in this positive angle structure, and to information about angled holonomy of the boundary tori.