7,2

This is the upper row of Table 1, p.9, of Bandieri, et al. We point out that there are no rigid genus two crystallizations with less than 14 vertices (i.e. with n = 7). 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." Karabas, Malicki and Nedela show that there exist exactly 78 non-homeomorphic, closed, orientable, prime 3-manifolds with Heegaard genus two, admitting a coloured triangulation with at most 42 tetrahedra. Each manifold M is identified by a suitable 6-tuple of non-negative integers, representing a minimal crystallization - hence a minimal coloured triangulation - of M. From such a 6-tuple, a presentation of the fundamental group and of the first homology group of M are easily obtained.

J. Karabas, P. Malicky, R. Nedela, Three-manifolds with Heegaard genus at most two represented by crystallisations with at most 42 vertices, Discrete Math. 307 (2007), no. 21, 2569-2590.

Paola Bandieri, Paola Cristofori and Carlo Gagliardi, A census of genus two 3-manifolds up to 42 coloured tetrahedra, Feb 3, 2009.

Sequence in context: A049015 A005250 A162762 this_sequence A039597 A000937 A167229

Adjacent sequences: A156094 A156095 A156096 this_sequence A156098 A156099 A156100

nonn

Jonathan Vos Post (jvospost3(AT)gmail.com), Feb 04 2009