OFFSET
7,2
COMMENTS
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.
REFERENCES
P. Bandieri et al., A census of genus-two 3-manifolds [with] up to 42 colored tetrahedra, Discrete Math., 310 (2010), 2469-2481.
LINKS
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.
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Jonathan Vos Post, Feb 04 2009
EXTENSIONS
Edited by N. J. A. Sloane, Sep 26 2010
STATUS
approved