Experimental Statistics of Veering Triangulations

ABSTRACT

Certain fibered hyperbolic three-manifolds admit a 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.

KEYWORDS:

• veering
• hyperbolic
• pseudo-Anosov
• fibered
• triangulation

2010 AMS SUBJECT CLASSIFICATION:

• Primary 57M50
• Secondary 57Q15

Acknowledgments

We are very grateful to Mark Bell for many helpful conversations about veering triangulations and his program flipper, and for excellent technical support for flipper! We also thank Saul Schleimer and Sam Taylor for illuminating conversations about veering triangulations, which at times helped guide further inquiry. Most of all we would like to thank Dave Futer for frequent conversations which were invaluable to the success of this project, and for much helpful guidance during the writing process. Additionally, we thank the referee for many helpful comments and suggestions.

Additional information

Funding

This research was supported in part by the National Science Foundation through major research instrumentation grant number CNS-09-58854.