A156098 Number of rigid genus-2 non-bipartite crystallizations of orientable 3-manifolds with 2n vertices.

1, 1, 1, 1, 2, 2, 3, 2, 6, 7, 9, 7, 12, 12, 16

Offset

7,5

Comments

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.

Links

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.

Crossrefs

A156097 enumerates all rigid bipartite examples.

Sequence in context: A095757 A144368 A094438 * A294933 A015996 A256564

Adjacent sequences: A156095 A156096 A156097 * A156099 A156100 A156101

Keyword

nonn,more

Author

Jonathan Vos Post, Feb 04 2009

Extensions

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

Status

approved