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%I #14 Nov 26 2014 20:19:04
%S 1,1,1,1,2,2,3,2,6,7,9,7,12,12,16
%N Number of rigid genus-2 non-bipartite crystallizations of orientable 3-manifolds with 2n vertices.
%C This is the lower row of Table 1, p.9, of Bandieri, et al. 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 colored triangulation with at most 42 tetrahedra. Each manifold M is identified by a suitable 6-tuple of nonnegative integers, representing a minimal crystallization - hence a minimal colored 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.
%H Paola Bandieri, Paola Cristofori and Carlo Gagliardi, <a href="http://arxiv.org/abs/0902.0492">A census of genus two 3-manifolds up to 42 coloured tetrahedra</a>, Feb 3, 2009.
%H P. Bandieri et al., <a href="http://dx.doi.org/10.1016/j.disc.2010.05.016">A census of genus-two 3-manifolds [with] up to 42 colored tetrahedra</a>, Discrete Math., 310 (2010), 2469-2481. [_N. J. A. Sloane_, Aug 26 2010]
%H J. Karabas, P. Malicky, R. Nedela, <a href="http://dx.doi.org/10.1016/j.disc.2006.11.017">Three-manifolds with Heegaard genus at most two represented by crystallisations with at most 42 vertices</a>, Discrete Math. 307 (2007), no. 21, 2569-2590.
%Y A156097 enumerates all rigid bipartite examples.
%K nonn,more
%O 7,5
%A _Jonathan Vos Post_, Feb 04 2009
%E Edited by _N. J. A. Sloane_, Sep 26 2010
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