Experimental statistics of veering triangulations

TL;DR

This paper presents experimental analysis of veering triangulations in fibered hyperbolic 3-manifolds, revealing their combinatorial structure and connections to topological invariants, advancing understanding of their properties.

Contribution

It provides new experimental insights into the combinatorial and topological features of veering triangulations in fibered hyperbolic 3-manifolds.

Findings

Detailed combinatorial patterns identified in veering triangulations

Correlations found between triangulation structure and manifold invariants

Enhanced understanding of the algorithmic construction process

Abstract

Certain fibered hyperbolic 3-manifolds admit a $\mathit{\text{layered veering triangulation}}$, which can be constructed algorithmically given the stable lamination of the monodromy. These triangulations were introduced by Agol in 2011, and have been further studied by several others in the years since. We obtain experimental results which shed light on the combinatorial structure of veering triangulations, and its relation to certain topological invariants of the underlying manifold.