On minimal ideal triangulations of cusped hyperbolic 3-manifolds

TL;DR

This paper extends previous methods to analyze minimal ideal triangulations of cusped hyperbolic 3-manifolds, demonstrating the minimality of monodromy ideal triangulations for certain fibered manifolds.

Contribution

It adapts techniques from closed 3-manifolds to ideal triangulations and proves minimality for a class of hyperbolic once-punctured torus bundles.

Findings

Monodromy ideal triangulations of hyperbolic once-punctured torus bundles are minimal.

The approach uses characterizations of low degree edges and cohomological properties.

The methods provide a blueprint for studying minimal ideal triangulations in cusped hyperbolic 3-manifolds.

Abstract

Previous work of the authors studies minimal triangulations of closed 3-manifolds using a characterisation of low degree edges, embedded layered solid torus subcomplexes and 1-dimensional $\mathbb{Z}_2$-cohomology. The underlying blueprint is now used in the study of minimal ideal triangulations. As an application, it is shown that the monodromy ideal triangulations of the hyperbolic once-punctured torus bundles are minimal.