Veering triangulations admit strict angle structures

TL;DR

This paper proves that all veering triangulations admit strict angle structures and provides an example of a veering taut triangulation that is not layered, expanding understanding of their geometric properties.

Contribution

It introduces a weaker notion of veering triangulation and demonstrates that all such triangulations admit strict angle structures, also answering a question about layered structures.

Findings

All veering triangulations admit strict angle structures

Provided an example of a veering taut triangulation that is not layered

Expanded the understanding of veering triangulations' geometric properties

Abstract

Agol recently introduced the concept of a veering taut triangulation, which is a taut triangulation with some extra combinatorial structure. We define the weaker notion of a "veering triangulation" and use it to show that all veering triangulations admit strict angle structures. We also answer a question of Agol, giving an example of a veering taut triangulation that is not layered.