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A156098 Number of rigid genus-2 non-bipartite crystallizations of orientable 3-manifolds with 2n vertices. 1
1, 1, 1, 1, 2, 2, 3, 2, 6, 7, 9, 7, 12, 12, 16 (list; graph; refs; listen; history; text; internal format)



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.


Table of n, a(n) for n=7..21.

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

P. Bandieri et al., A census of genus-two 3-manifolds [with] up to 42 colored tetrahedra, Discrete Math., 310 (2010), 2469-2481. [N. J. A. Sloane, Aug 26 2010]

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.


A156097 enumerates all rigid bipartite examples.

Sequence in context: A095757 A144368 A094438 * A294933 A015996 A256564

Adjacent sequences:  A156095 A156096 A156097 * A156099 A156100 A156101




Jonathan Vos Post, Feb 04 2009


Edited by N. J. A. Sloane, Sep 26 2010



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