Classifying Genus Two 3-Manifolds up to 34 Tetrahedra

In this paper, we present a catalogue of all genus two 3-manifolds admitting a contracted triangulation with at most 34 simplexes. Then we give a complete classification of the above manifolds.Mathematics Subject Classifications (2000) 57M05, 57N10, 57M15.Work performed under the auspicies of the G.N.S.A.G.A. of the C.N.R. (National Research Council of Italy) and financially supported by M.I.U.R. of Italy (project Strutture geometriche delle varietà reali e complesse).