Structures of small closed non-orientable 3-manifold triangulations
Abstract
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.
Keywords
Cite
@article{arxiv.math/0311113,
title = {Structures of small closed non-orientable 3-manifold triangulations},
author = {Benjamin A. Burton},
journal= {arXiv preprint arXiv:math/0311113},
year = {2010}
}
Comments
30 pages, 46 figures; v2: fixed off-by-one errors in the formulae for Theorems 4.6 and 4.9, plus general proofreading updates