Z2-Thurston Norm and Complexity of 3-Manifolds, II

TL;DR

This paper establishes new bounds on the complexity of closed 3-manifolds and characterizes those that achieve these bounds, including infinite families of minimal triangulations of specific Seifert fibred spaces.

Contribution

It introduces novel bounds on 3-manifold complexity and characterizes manifolds that attain these bounds, with applications to minimal triangulations of Seifert fibred spaces.

Findings

New bounds on 3-manifold complexity

Characterization of manifolds realizing these bounds

First infinite families of minimal triangulations for certain Seifert fibred spaces

Abstract

In this sequel to earlier papers by three of the authors, we obtain a new bound on the complexity of a closed 3--manifold, as well as a characterisation of manifolds realising our complexity bounds. As an application, we obtain the first infinite families of minimal triangulations of Seifert fibred spaces modelled on Thurston's geometry $\widetilde{\text{SL}_2(\mathbb{R})}.$