Structures of small closed non-orientable 3-manifold triangulations

Details Structures of small closed non-orientable 3-manifold triangulations Structures of small closed non-orientable 3-manifold triangulations

2003-11-07

arxiv.org/abs/math/0311113v2

Journal of Knot Theory and Its Ramifications 16 (2007), no. 5, 545-574

Mathematics

Geometric Topology

30 pages, 46 figures; v2: fixed off-by-one errors in the formulae for Theorems 4.6 and 4.9, plus general proofreading updates

Scientific paper

10.1142/S0218216507005439

A census is presented of all closed non-orientable 3-manifold triangulations formed from at most seven tetrahedra satisfying the additional constraints of minimality and P^2-irreducibility. The eight different 3-manifolds represented by these 41 different triangulations are identified and described in detail, with particular attention paid to the recurring combinatorial structures that are shared amongst the different triangulations. Using these recurring structures, the resulting triangulations are generalised to infinite families that allow similar triangulations of additional 3-manifolds to be formed. Algorithms and techniques used in constructing the census are included.

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