7,5

This is the lower 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.

Cf. A156097 enumerates all rigid bipartite examples.

Sequence in context: A095757 A144368 A094438 this_sequence A015996 A092976 A084705

Adjacent sequences: A156095 A156096 A156097 this_sequence A156099 A156100 A156101

nonn

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