Classifying genus two 3-manifolds up to 34 tetrahedra (Q1776820)

The authors present a catalogue of all genus two 3-manifolds admitting a contracted triangulation with at most 32 simplexes. The main theorem of the article states: There are exactly 26 closed, connected orientable, prime 3-manifolds of genus two admitting a crystallization with at most 34 vertices. A \textit{crystallization} of a 3-manifold is a contracted \((n+1)\)-colored graph representing the 3-mainfold, where a vertex of the graph corresponds to a simplex. In the article the authors give a complete classification of the above 26 manifolds.