Enumeration of non-orientable 3-manifolds using face pairing graphs and union-find

Details Enumeration of non-orientable 3-manifolds using face pairing graphs and union-find Enumeration of non-orientable 3-manifolds using face pairing graphs and union-find

2006-04-27

arxiv.org/abs/math/0604584v1

Discrete and Computational Geometry 38 (2007), no. 3, 527-571

Mathematics

Geometric Topology

37 pages, 34 figures

Scientific paper

10.1007/s00454-007-1307-x

Drawing together techniques from combinatorics and computer science, we improve the census algorithm for enumerating closed minimal P^2-irreducible 3-manifold triangulations. In particular, new constraints are proven for face pairing graphs, and pruning techniques are improved using a modification of the union-find algorithm. Using these results we catalogue all 136 closed non-orientable P^2-irreducible 3-manifolds that can be formed from at most ten tetrahedra.

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