A new family of minimal ideal triangulations of cusped hyperbolic 3-manifolds

TL;DR

This paper introduces an infinite family of minimal ideal triangulations for certain cusped hyperbolic 3-manifolds, extending previous bounds and demonstrating their attainability through Dehn fillings on a specific link.

Contribution

It presents a new infinite family of minimal ideal triangulations for cusped hyperbolic 3-manifolds that achieve the known lower bound on complexity.

Findings

Established an infinite family of minimal triangulations.

Demonstrated these triangulations attain the lower bound on complexity.

Extended previous results to new classes of 3-manifolds.

Abstract

Previous work of the authors with Bus Jaco determined a lower bound on the complexity of cusped hyperbolic 3-manifolds and showed that it is attained by the monodromy ideal triangulations of once-punctured torus bundles. This paper exhibits an infinite family of minimal ideal triangulations of Dehn fillings on the link $8^3_9$ that also attain this lower bound on complexity.