A census of genus two 3-manifolds up to 42 coloured tetrahedra

TL;DR

This paper extends the classification of orientable prime 3-manifolds of Heegaard genus two, triangulated with up to 42 coloured tetrahedra, including non-orientable cases, providing a comprehensive census.

Contribution

It improves and extends previous classification results to include non-orientable 3-manifolds within the same triangulation complexity bound.

Findings

Complete census of genus two 3-manifolds up to 42 tetrahedra

Includes non-orientable cases in the classification

Refines previous orientable-only results

Abstract

We improve and extend to the non-orientable case a recent result of Karabas, Malicki and Nedela concerning the classification of all orientable prime 3-manifolds of Heegaard genus two, triangulated with at most 42 coloured tetrahedra.