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A156097
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Number of rigid genus-2 bipartite crystallizations of orientable 3-manifolds with 2n vertices.
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1
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1, 2, 4, 6, 8, 14, 18, 23, 38, 47, 58, 79, 118, 128, 159
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OFFSET
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7,2
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COMMENTS
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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.
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REFERENCES
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P. Bandieri et al., A census of genus-two 3-manifolds [with] up to 42 colored tetrahedra, Discrete Math., 310 (2010), 2469-2481.
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LINKS
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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.
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.
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CROSSREFS
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Cf. A156098.
Sequence in context: A049015 A005250 A162762 * A288793 A039597 A167229
Adjacent sequences: A156094 A156095 A156096 * A156098 A156099 A156100
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KEYWORD
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nonn,more
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AUTHOR
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Jonathan Vos Post, Feb 04 2009
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EXTENSIONS
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Edited by N. J. A. Sloane, Sep 26 2010
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STATUS
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approved
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