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A156097 Number of rigid genus-2 bipartite crystallizations of orientable 3-manifolds with 2n vertices. 1


%S 1,2,4,6,8,14,18,23,38,47,58,79,118,128,159

%N Number of rigid genus-2 bipartite crystallizations of orientable 3-manifolds with 2n vertices.

%C This is the upper 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.

%D P. Bandieri et al., A census of genus-two 3-manifolds [with] up to 42 colored tetrahedra, Discrete Math., 310 (2010), 2469-2481.

%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 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 Cf. A156098.

%K nonn,more

%O 7,2

%A _Jonathan Vos Post_, Feb 04 2009

%E Edited by _N. J. A. Sloane_, Sep 26 2010

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